Mauro Ursino

Comparison of different cortical connectivity estimators for high-resolution EEG recordings

The aim of this work is to characterize quantitatively the performance of a body of techniques in the frequency domain for the estimation of cortical connectivity from high‐resolution EEG recordings in different operative conditions commonly encountered in practice. Connectivity pattern estimators investigated are the Directed Transfer Function (DTF), its modification known as direct DTF (dDTF) and the Partial Directed Coherence (PDC). Predefined patterns of cortical connectivity were simulated and then retrieved by the application of the DTF, dDTF, and PDC methods. Signal‐to‐noise ratio (SNR) and length (LENGTH) of EEG epochs were studied as factors affecting the reconstruction of the imposed connectivity patterns. Reconstruction quality and error rate in estimated connectivity patterns were evaluated by means of some indexes of quality for the reconstructed connectivity pattern. The error functions were statistically analyzed with analysis of variance (ANOVA). The whole methodology was then applied to high‐resolution EEG data recorded during the well‐known Stroop paradigm. Simulations indicated that all three methods correctly estimated the simulated connectivity patterns under reasonable conditions. However, performance of the methods differed somewhat as a function of SNR and LENGTH factors. The methods were generally equivalent when applied to the Stroop data. In general, the amount of available EEG affected the accuracy of connectivity pattern estimations. Analysis of 27 s of nonconsecutive recordings with an SNR of 3 or more ensured that the connectivity pattern could be accurately recovered with an error below 7% for the PDC and 5% for the DTF. In conclusion, functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in most EEG recordings by combining high‐resolution EEG techniques, linear inverse estimation of the cortical activity, and frequency domain multivariate methods such as PDC, DTF, and dDTF. Hum. Brain Mapp, 2007.

Interaction between carotid baroregulation and the pulsating heart: a mathematical model.

A mathematical model of short-term arterial pressure control by the carotid baroreceptors in pulsatile conditions is presented. The model includes an elastance variable description of the left and right heart, the systemic (splanchnic and extrasplanchnic) and pulmonary circulations, the afferent carotid baroreceptor pathway, the sympathetic and vagal efferent activities, and the action of several effector mechanisms. The latter mechanisms work, in response to sympathetic and vagal action, by modifying systemic peripheral resistances, systemic venous unstressed volumes, heart period, and end-systolic elastances. The model is used to simulate the interaction among the carotid baroreflex, the pulsating heart, and the effector responses in different experiments. In all cases, there has been satisfactory agreement between model and experimental results. Experimental data on heart rate control can be explained fairly well by assuming that the sympathetic-parasympathetic systems interact linearly on the heart period. The carotid baroreflex can significantly modulate the cardiac function curve. However, this effect is masked in vivo by changes in arterial and atrial pressures. During heart pacing, cardiac output increases with frequency at moderate levels of heart rate and then fails to increase further because of a reduction in stroke volume. Shifting from nonpulsatile to pulsatile perfusion of the carotid sinuses decreases the overall baroreflex gain and significantly modifies operation of the carotid baroreflex. Finally, a sensitivity analysis suggests that venous unstressed volume control plays the major role in the early hemodynamic response to acute hemorrhage, whereas systemic resistance and heart rate controls are a little less important.A mathematical model of short-term arterial pressure control by the carotid baroreceptors in pulsatile conditions is presented. The model includes an elastance variable description of the left and right heart, the systemic (splanchnic and extrasplanchnic) and pulmonary circulations, the afferent carotid baroreceptor pathway, the sympathetic and vagal efferent activities, and the action of several effector mechanisms. The latter mechanisms work, in response to sympathetic and vagal action, by modifying systemic peripheral resistances, systemic venous unstressed volumes, heart period, and end-systolic elastances. The model is used to simulate the interaction among the carotid baroreflex, the pulsating heart, and the effector responses in different experiments. In all cases, there has been satisfactory agreement between model and experimental results. Experimental data on heart rate control can be explained fairly well by assuming that the sympathetic-parasympathetic systems interact linearly on the heart period. The carotid baroreflex can significantly modulate the cardiac function curve. However, this effect is masked in vivo by changes in arterial and atrial pressures. During heart pacing, cardiac output increases with frequency at moderate levels of heart rate and then fails to increase further because of a reduction in stroke volume. Shifting from nonpulsatile to pulsatile perfusion of the carotid sinuses decreases the overall baroreflex gain and significantly modifies operation of the carotid baroreflex. Finally, a sensitivity analysis suggests that venous unstressed volume control plays the major role in the early hemodynamic response to acute hemorrhage, whereas systemic resistance and heart rate controls are a little less important.

A mathematical study of human intracranial hydrodynamics. Part 1. The cerebrospinal fluid pulse pressure

An original mathematical model of human intracranial hydrodynamics is proposed. Equations able to mimic the behavior of the intracranial arterial vascular bed, intracranial venous vascular bed, cerebrospinal fluid absorption and production processes, and the constancy of overall intracranial volume are separately presented and discussed. The model parameters were given normal values computed using physiological considerations and recent anatomical data. In this paper the model is used to simulate the genesis and morphology of the intracranial pressure pulse wave. In particular, dependence of the intracranial pressure pulse amplitude on mean intracranial pressure, obtained from the model, shows excellent agreement with recent experimental findings. The model explains the intracranial pressure pulse wave as the result of the pulsating changes in cerebral blood volume (related to cerebrovascular compliance) which occur within a rigid space (i.e., the craniospinal compartment). At low and medium values of intracranial pressure, the intracranial pressure pulse amplitude mainly reflects the cerebral pressure-volume relationship. However, during severe intracranial hypertension, an abrupt increase in the cerebrovascular compliance becomes evident, which is reflected in an abrupt increase in the intracranial pressure pulse wave.

A mathematical study of some biomechanical factors affecting the oscillometric blood pressure measurement

A mathematical lumped parameter model of the oscillometric technique for indirect blood pressure measurement is presented. The model includes cuff compliance, pressure transmission from the cuff to the brachial artery through the soft tissue of the arm, and the biomechanics of the brachial artery both at positive and negative transmural pressure values. The main aspects of oscillometry are simulated i.e., the increase in cuff pressure pulsatility during cuff deflation manoeuvres, the existence of a point of maximum pulsations (about 1.5 mmHg) at a cuff pressure close to mean arterial pressure, and the characteristic ratios for cuff pressure pulsatility at systole and diastole (0.52 and 0.70, respectively, with this model, using basal parameters and an individual set of data for the arterial pressure waveform). Subsequently, the model is used to examine how alterations in some biomechanical factors may prejudice the accuracy of pressure measurement. Numerical simulations indicate that alterations in wall viscoelastic properties and in arterial pressure pulse amplitude may significantly affect the accuracy of pressure estimates, leading to errors as great as 15-20% in the computation of diastolic and systolic arterial pressure. By contrast, changes in arterial pressure mean value and cuff compliance do not seem to have significant influence on the measurement. Evaluation of mean arterial pressure through a characteristic ratio is not robust and may lead to misleading results. Mean arterial pressure may be better evaluated as the lowest pressure at which cuff pulse amplitude reaches a plateau. The obtained results may help to explain the nature of errors which usually limit the reliability of arterial pressure measurement (for instance in the elderly).

Tracking the Time-Varying Cortical Connectivity Patterns by Adaptive Multivariate Estimators

The directed transfer function (DTF) and the partial directed coherence (PDC) are frequency-domain estimators that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods is based on the multivariate autoregressive modelling (MVAR) of time series, which requires the stationarity of the signals. In this way, transient pathways of information transfer remains hidden. The objective of this study is to test a time-varying multivariate method for the estimation of rapidly changing connectivity relationships between cortical areas of the human brain, based on DTF/PDC and on the use of adaptive MVAR modelling (AMVAR) and to apply it to a set of real high resolution EEG data. This approach will allow the observation of rapidly changing influences between the cortical areas during the execution of a task. The simulation results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of signal-to-noise ratio (SNR) ad number of trials. An SNR of Ave and a number of trials of at least 20 provide a good accuracy in the estimation. After testing the method by the simulation study, we provide an application to the cortical estimations obtained from high resolution EEG data recorded from a group of healthy subject during a combined foot-lips movement and present the time-varying connectivity patterns resulting from the application of both DTF and PDC. Two different cortical networks were detected with the proposed methods, one constant across the task and the other evolving during the preparation of the joint movement.

Interaction among autoregulation, CO2 reactivity, and intracranial pressure: a mathematical model

The relationships among cerebral blood flow, cerebral blood volume, intracranial pressure (ICP), and the action of cerebrovascular regulatory mechanisms (autoregulation and CO2 reactivity) were investigated by means of a mathematical model. The model incorporates the cerebrospinal fluid (CSF) circulation, the intracranial pressure-volume relationship, and cerebral hemodynamics. The latter is based on the following main assumptions: the middle cerebral arteries behave passively following transmural pressure changes; the pial arterial circulation includes two segments (large and small pial arteries) subject to different autoregulation mechanisms; and the venous cerebrovascular bed behaves as a Starling resistor. A new aspect of the model exists in the description of CO2 reactivity in the pial arterial circulation and in the analysis of its nonlinear interaction with autoregulation. Simulation results, obtained at constant ICP using various combinations of mean arterial pressure and CO2 pressure, substantially support data on cerebral blood flow and velocity reported in the physiological literature concerning both the separate effects of CO2 and autoregulation and their nonlinear interaction. Simulations performed in dynamic conditions with varying ICP underline the existence of a significant correlation between ICP dynamics and cerebral hemodynamics in response to CO2 changes. This correlation may significantly increase in pathological subjects with poor intracranial compliance and reduced CSF outflow. In perspective, the model can be used to study ICP and blood velocity time patterns in neurosurgical patients in order to gain a deeper insight into the pathophysiological mechanisms leading to intracranial hypertension and secondary brain damage.The relationships among cerebral blood flow, cerebral blood volume, intracranial pressure (ICP), and the action of cerebrovascular regulatory mechanisms (autoregulation and CO2 reactivity) were investigated by means of a mathematical model. The model incorporates the cerebrospinal fluid (CSF) circulation, the intracranial pressure-volume relationship, and cerebral hemodynamics. The latter is based on the following main assumptions: the middle cerebral arteries behave passively following transmural pressure changes; the pial arterial circulation includes two segments (large and small pial arteries) subject to different autoregulation mechanisms; and the venous cerebrovascular bed behaves as a Starling resistor. A new aspect of the model exists in the description of CO2 reactivity in the pial arterial circulation and in the analysis of its nonlinear interaction with autoregulation. Simulation results, obtained at constant ICP using various combinations of mean arterial pressure and CO2 pressure, substantially support data on cerebral blood flow and velocity reported in the physiological literature concerning both the separate effects of CO2 and autoregulation and their nonlinear interaction. Simulations performed in dynamic conditions with varying ICP underline the existence of a significant correlation between ICP dynamics and cerebral hemodynamics in response to CO2 changes. This correlation may significantly increase in pathological subjects with poor intracranial compliance and reduced CSF outflow. In perspective, the model can be used to study ICP and blood velocity time patterns in neurosurgical patients in order to gain a deeper insight into the pathophysiological mechanisms leading to intracranial hypertension and secondary brain damage.

Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data

The aim of this paper is to test a technique called partial directed coherence (PDC) and its modification (squared PDC; sPDC) for the estimation of human cortical connectivity by means of simulation study, in which both PDC and sPDC were studied by analysis of variance. The statistical analysis performed returned that both PDC and sPDC are able to estimate correctly the imposed connectivity patterns when data exhibit a signal-to-noise ratio of at least 3 and a length of at least 27 s of nonconsecutive recordings at 250 Hz of sampling rate, equivalent, more generally, to 6750 data samples

A mathematical model of the relationship between cerebral blood volume and intracranial pressure changes: The generation of plateau waves

The relationship between intracranial pressure (ICP), cerebral blood volume (CBV), cerebrospinal fluid dynamics, and the action of cerebral blood-flow (CBF) regulatory mechanisms is examined in this work with the help of an original mathematical model. In building the model, particular emphasis is placed on reproducing the mechanical properties of proximal cerebral arteries and small pial arterioles, and their active regulatory response to perfusion pressure and cerebral blood flow changes.The model allows experimental results on cerebral vessel dilatation and cerebral blood-flow regulation, following cerebral perfusion pressure decrease, to be satisfactorily reproduced. Moreover, the effect of cerebral blood volume changes—induced by autoregulatory adjustments — on the intracranial pressure time pattern can be examined at different levels of arterial hypotension.The results obtained with normal parameter values demonstrate that, at the lower lumits of autoregulation, when dilatation of small arterioles becomes maximal, the increase in cerebral blood volume can cause a significant, transient increase in intracranial pressure. This antagonism between intracranial pressure and autoregulatory adjustments can lead to instability of the intracranial system in pathological conditions. In particular, analysis of the linearized system “in the small” demonstrates that an impairment in cerebrospinal fluid (CSF) reabsorption, a decrease in intracranial compliance and a high-regulatory capacity of the cerebrovascular bed are all conditions which can lead the system equilibrium to become unstable (i.e., the real part of at least one eigenvalue to turn out positive). Accordingly, mathematical simulation “in the large,” in the above-mentioned conditions, exhibits intracranial pressure periodic fluctuations which closely resemble, in amplitude, duration, frequency and shape, the well-known Lundberg A-waves (or plateau waves).

Intracranial pressure dynamics in patients with acute brain damage: a critical analysis with the aid of a mathematical model

The time pattern of intracranial pressure (ICP) in response to typical clinical tests (i.e., bolus injection and bolus withdrawal of 1 to 4 mL of saline in the craniospinal space) was studied in 18 patients with acute brain damage by means of a mathematical model. The model includes the main biomechanical factors assumed to affect intracranial pressure, particularly cerebrospinal fluid (CSF) dynamics, intracranial compliance, and cerebral hemodynamics. Best fitting between model simulation curves and clinical tracings was achieved using the Powell minimization algorithm and a least-square criterion function. The simulation results demonstrate that, in most patients, the ICP time pattern cannot be explained merely on the basis of CSF dynamics but also requires consideration of the contribution of cerebral hemodynamics and blood volume alterations. In particular, only in a few patients (about 40% of total) the ICP monotonically returns toward baseline following the clinical maneuver. In most of the examined cases (about 60%), ICP exhibits an anomalous response to the same maneuver, characterized by a delayed increase after bolus injection and a delayed decrease after withdrawal. The model is able to explain these responses, imputing them to active intracranial blood volume changes induced by mechanisms controlling cerebral blood flow. Finally, the role of the main intracranial biomechanical parameters in the genesis of the ICP time pattern is discussed and a comparison with previous theoretical studies performed.<<ETX>>

Correlations among intracranial pulsatility, intracranial hemodynamics, and transcranial doppler wave form: Literature review and hypothesis for future studies

&NA; In the present work, the major correlations among cerebrospinal fluid (CSF) pulsatility, cerebral hemodynamic changes. the action of mechanisms regulating cerebral blood flow and cerebral blood volume. and the main aspects of the intracranial basal artery transcranial Doppler wave form are critically examined. CSF pulsatility is a consequence of rigidity of the craniospinal compartment and the pulsating changes in cerebral blood volume. At low and medium intracranial pressures (ICPs), changes in CSF pulsatility are mainly the result of changes in craniospinal elastance. During severe intracranial hypertension. however, CSF pulse pressure reflects an abrupt increase in cerebrovascular (i.e., cerebral vessel) compliance. The mechanisms controlling cerebral blood flow and cerebral blood volume affect CSF pulsatility through both an alteration in craniospinal blood volume and a change in vascular wall pulsatility. Examination of the main parameters of the Doppler velocity pattern (maximal systolic blood velocity, diastolic blood velocity, and peak to peak pulsatility index) in cerebral basal arteries reveals a significant alteration in the velocity wave form during severe ICP increase (above 60 mm Hg). During moderate ICP increase, when cerebral regulatory mechanisms are effective, the Doppler velocity pattern is not significantly affected by ICP changes.