A new hemodynamic model for the study of cerebral venous outflow.

We developed a mathematical model of the cerebral venous outflow for the simulation of the average blood flows and pressures in the main drainage vessels of the brain. The main features of the model are that it includes a validated model for the simulation of the intracranial circulation and it accounts for the dependence of the hydraulic properties of the jugular veins with respect to the gravity field, which makes it an useful tool for the study of the correlations between extracranial blood redistributions and changes in the intracranial environment. The model is able to simulate the average pressures and flows in different points of the jugular ducts, taking into account the amount of blood coming from the anastomotic connections; simulate how the blood redistribution due to change of posture affects flows and pressures in specific points of the system; and simulate redistributions due to stenotic patterns. Sensitivity analysis to check the robustness of the model was performed. The model reproduces average physiologic behavior of the jugular, vertebral, and cerebral ducts in terms of pressures and flows. In fact, jugular flow drops from ∼11.7 to ∼1.4 ml/s in the passage from supine to standing. At the same time, vertebral flow increases from 0.8 to 3.4 ml/s, while cerebral blood flow, venous sinuses pressure, and intracranial pressure are constant around the average value of 12.5 ml/s, 6 mmHg, and 10 mmHg, respectively. All these values are in agreement with literature data.

A thalamo-cortical neural mass model for the simulation of brain rhythms during sleep.

Cortico-thalamic interactions are known to play a pivotal role in many brain phenomena, including sleep, attention, memory consolidation and rhythm generation. Hence, simple mathematical models that can simulate the dialogue between the cortex and the thalamus, at a mesoscopic level, have a great cognitive value. In the present work we describe a neural mass model of a cortico-thalamic module, based on neurophysiological mechanisms. The model includes two thalamic populations (a thalamo-cortical relay cell population, TCR, and its related thalamic reticular nucleus, TRN), and a cortical column consisting of four connected populations (pyramidal neurons, excitatory interneurons, inhibitory interneurons with slow and fast kinetics). Moreover, thalamic neurons exhibit two firing modes: bursting and tonic. Finally, cortical synapses among pyramidal neurons incorporate a disfacilitation mechanism following prolonged activity. Simulations show that the model is able to mimic the different patterns of rhythmic activity in cortical and thalamic neurons (beta and alpha waves, spindles, delta waves, K-complexes, slow sleep waves) and their progressive changes from wakefulness to deep sleep, by just acting on modulatory inputs. Moreover, simulations performed by providing short sensory inputs to the TCR show that brain rhythms during sleep preserve the cortex from external perturbations, still allowing a high cortical activity necessary to drive synaptic plasticity and memory consolidation. In perspective, the present model may be used within larger cortico-thalamic networks, to gain a deeper understanding of mechanisms beneath synaptic changes during sleep, to investigate the specific role of brain rhythms, and to explore cortical synchronization achieved via thalamic influences.

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 neural mass model of interconnected regions simulates rhythm propagation observed via TMS-EEG.

Knowledge of cortical rhythms represents an important aspect of modern neuroscience, to understand how the brain realizes its functions. Recent data suggest that different regions in the brain may exhibit distinct electroencephalogram (EEG) rhythms when perturbed by Transcranial Magnetic Stimulation (TMS) and that these rhythms can change due to the connectivity among regions. In this context, in silico simulations may help the validation of these hypotheses that would be difficult to be verified in vivo. Neural mass models can be very useful to simulate specific aspects of electrical brain activity and, above all, to analyze and identify the overall frequency content of EEG in a cortical region of interest (ROI). In this work we implemented a model of connectivity among cortical regions to fit the impulse responses in three ROIs recorded during a series of TMS/EEG experiments performed in five subjects and using three different impulse intensities. In particular we investigated Brodmann Area (BA) 19 (occipital lobe), BA 7 (parietal lobe) and BA 6 (frontal lobe). Results show that the model can reproduce the natural rhythms of the three regions quite well, acting on a few internal parameters. Moreover, the model can explain most rhythm changes induced by stimulation of another region, and inter-subject variability, by estimating just a few long-range connectivity parameters among ROIs.

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 five 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.

dfpk: An R-package for Bayesian dose-finding designs using pharmacokinetics (PK) for phase I clinical trials.

BACKGROUND AND OBJECTIVE: Dose-finding, aiming at finding the maximum tolerated dose, and pharmacokinetics studies are the first in human studies in the development process of a new pharmacological treatment. In the literature, to date only few attempts have been made to combine pharmacokinetics and dose-finding and to our knowledge no software implementation is generally available. In previous papers, we proposed several Bayesian adaptive pharmacokinetics-based dose-finding designs in small populations. The objective of this work is to implement these dose-finding methods in an R package, called dfpk. METHODS: All methods were developed in a sequential Bayesian setting and Bayesian parameter estimation is carried out using the rstan package. All available pharmacokinetics and toxicity data are used to suggest the dose of the next cohort with a constraint regarding the probability of toxicity. Stopping rules are also considered for each method. The ggplot2 package is used to create summary plots of toxicities or concentration curves. RESULTS: For all implemented methods, dfpk provides a function (nextDose) to estimate the probability of efficacy and to suggest the dose to give to the next cohort, and a function to run trial simulations to design a trial (nsim). The sim.data function generates at each dose the toxicity value related to a pharmacokinetic measure of exposure, the AUC, with an underlying pharmacokinetic one compartmental model with linear absorption. It is included as an example since similar data-frames can be generated directly by the user and passed to nsim. CONCLUSION: The developed user-friendly R package dfpk, available on the CRAN repository, supports the design of innovative dose-finding studies using PK information.

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.

Validation of a Hemodynamic Model for the Study of the Cerebral Venous Outflow System Using MR Imaging and Echo-Color Doppler Data.

BACKGROUND AND PURPOSE: A comprehensive parameter model was developed to investigate correlations between cerebral hemodynamics and alterations in the extracranial venous circulation due to posture changes and/or extracranial venous obstruction (stenosis). The purpose of this work was to validate the simulation results by using MR imaging and echo-color Doppler experimental blood flow data in humans. MATERIALS AND METHODS: To validate the model outcomes, we used supine average arterial and venous extracerebral blood flow, obtained by using phase-contrast MR imaging from 49 individuals with stenosis in the acquisition plane at the level of the disc between the second and third vertebrae of the left internal jugular vein, 20 with stenosis in the acquisition plane at the level of the disc between the fifth and sixth vertebrae of the right internal jugular vein, and 38 healthy controls without stenosis. Average data from a second group of 10 healthy volunteers screened with an echo-color Doppler technique were used to evaluate flow variations due to posture change. RESULTS: There was excellent agreement between experimental and simulated supine flows. Every simulated CBF fell inside the standard error from the corresponding average experimental value, as well as most of the simulated extracerebral arterial flow (extracranial blood flow from the head and face, measured at the level of the disc between second and third vertebrae) and venous flows. Simulations of average jugular and vertebral blood flow variations due to a change of posture from supine to upright also matched the experimental data. CONCLUSIONS: The good agreement between simulated and experimental results means that the model can correctly reproduce the main factors affecting the extracranial circulation and could be used to study other types of stenotic conditions not represented by the experimental data.

Clinical study of continuous non-invasive cerebrovascular autoregulation monitoring in neurosurgical ICU.

Ultrasonic "time-of-flight" monitor (Vittamed) was used for continuous monitoring of intracranial blood volume (IBV) pulse, respiratory, slow waves and cerebrovascular autoregulation (CA). The objectives are to compare of invasively and non-invasively monitored slow intracranial waves and CA of ICU patients and to evaluate the phase shift between ABP and IBV respiratory waves as a possible estimator of CA. CA monitoring has been performed in 13 patients with severe TBI (age mean/range 30.5/(18-64)). Data were collected from 87 one-hour sessions of simultaneous invasive and non-invasive wave monitoring and from 53 one-hour sessions of invasive and non-invasive CA monitoring. High correlation (R > 0.9) has been obtained between invasively and non-invasively recorded intracranial slow waves. Bland Altman difference between invasively and non-invasively recorded intracranial slow waves is clinically not significant (mean =-0.07, SD = 0.089, alpha = 0.05). Agreement has been confirmed between invasive and non-invasive CA monitoring data in a wide range of R = [-0.85; +0.96]. Hypothesis of the coincidence of invasive and non-invasive CA assessment is accepted (p < 0.05). Phase shift monitoring of permanent respiratory ABP waves and IBV waves permit continuous non-invasive CA estimation without unnatural physical or pharmacological stimulations of CA system.

A simulation model to study the role of the extracranial venous drainage pathways in intracranial hemodynamics.

Alterations in the extracranial venous circulation due to posture changes, and/or extracranial venous obstructions in patients with vascular diseases, can have important implications on cerebral hemodynamics. A hemodynamic model for the study of cerebral venous outflow was developed to investigate the correlations between extracranial blood redistributions and changes in the intracranial environment. Flow data obtained with both magnetic resonance (MR) and Echo-Color Doppler (ECD) technique are used to validate the model. The very good agreement between simulated supine and upright flows and experimental results means that the model can correctly reproduce the main factors affecting the extracranial venous circulation.

A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics.

A simple mathematical model of intracranial pressure (ICP) dynamics oriented to clinical practice is presented. It includes the hemodynamics of the arterial-arteriolar cerebrovascular bed, cerebrospinal fluid (CSF) production and reabsorption processes, the nonlinear pressure-volume relationship of the craniospinal compartment, and a Starling resistor mechanism for the cerebral veins. Moreover, arterioles are controlled by cerebral autoregulation mechanisms, which are simulated by means of a time constant and a sigmoidal static characteristic. The model is used to simulate interactions between ICP, cerebral blood volume, and autoregulation. Three different related phenomena are analyzed: the generation of plateau waves, the effect of acute arterial hypotension on ICP, and the role of cerebral hemodynamics during pressure-volume index (PVI) tests. Simulation results suggest the following: 1) ICP dynamics may become unstable in patients with elevated CSF outflow resistance and decreased intracranial compliance, provided cerebral autoregulation is efficient. Instability manifests itself with the occurrence of self-sustained plateau waves. 2) Moderate acute arterial hypotension may have completely different effects on ICP, depending on the value of model parameters. If physiological compensatory mechanisms (CSF circulation and intracranial storage capacity) are efficient, acute hypotension has only negligible effects on ICP and cerebral blood flow (CBF). If these compensatory mechanisms are poor, even modest hypotension may induce a large transient increase in ICP and a significant transient reduction in CBF, with risks of secondary brain damage. 3) The ICP response to a bolus injection (PVI test) is sharply affected, via cerebral blood volume changes, by cerebral hemodynamics and autoregulation. We suggest that PVI tests may be used to extract information not only on intracranial compliance and CSF circulation, but also on the status of mechanisms controlling CBF.

Intracranial pressure dynamics in patients with acute brain damage.

The time pattern of intracranial pressure (ICP) during pressure-volume index (PVI) tests was analyzed in 20 patients with severe acute brain damage by means of a simple mathematical model. In most cases, a satisfactory fitting between model response and patient data was achieved by adjusting only four parameters: the cerebrospinal fluid (CSF) outflow resistance, the intracranial elastance coefficient, and the gain and time constant of cerebral autoregulation. The correlation between the parameter estimates was also analyzed to elucidate the main mechanisms responsible for ICP changes in each patient. Starting from information on the estimated parameter values and their correlation, the patients were classified into two main classes: those with weak autoregulation (8 of 20 patients) and those with strong autoregulation (12 of 20 patients). In the first group of patients, ICP mainly reflects CSF circulation and passive cerebral blood volume changes. In the second group, ICP exhibits paradoxical responses attributable to active changes in cerebral blood volume. Moreover, in two patients of the second group, the time constant of autoregulation is significantly increased (>40 s). The correlation between the parameter estimates was significantly different in the two groups of patients, suggesting the existence of different mechanisms responsible for ICP changes. Moreover, analysis of the correlation between the parameter estimates might give information on the directions of parameter changes that have a greater impact on ICP.

Mechanisms of cerebral blood flow regulation.

The main aspects of cerebral blood flow regulation are analyzed in the present work. Particular emphasis is given to the biophysical aspects of the cerebral circulation and to problems related with mathematical modeling. Throughout the present work a systemic approach is used, i.e., the intracranial circulation is regarded as a complex system, the behavior of which derives from the interaction and superimposition of several concomitant effects. A brief historical review of the major experimental results on cerebrovascular regulation is presented. Subsequently, the functional structure of the cerebrovascular bed is analyzed in detail and the major feedback regulatory mechanisms, which are now assumed to work on the cerebral circulation (that is, the chemical, the myogenic and the neurogenic ones) are separately examined, according to recently published literature. Mathematical models able to describe all these phenomena are presented and their advantages, limitations, and possible role in physiological investigation discussed. Finally, attention is focused on the major problems which still deserve further studies and on possible lines for future investigations.

Impact of cerebral perfusion pressure and autoregulation on intracranial dynamics: a modeling study.

OBJECTIVE: The aim of this work was to study the impact of acute cerebral perfusion pressure (CPP) changes and autoregulation on cerebral hemodynamics, intracranial pressure (ICP), and estimation of the pressure-volume index (PVI) and the possible involvement of these factors in the development of secondary brain damage. METHODS: The study was performed by using a mathematical model of intracranial hemodynamics and cerebrospinal fluid (CSF) dynamics. The model includes the biomechanics of proximal and distal arterial intracranial vessels, cerebral veins, and CSF circulation, the intracranial pressure-volume relationship, and the action of autoregulation mechanisms on proximal and distal vessels. RESULTS: In the case of normal intracranial dynamics, lowering mean systemic arterial pressure (SAP) in the range of 100 to 60 mm Hg causes only a mild ICP increase (+1-2 mm Hg). In contrast, in the case of severe impairment of intracranial dynamics (reductions in CSF outflow and storage capacity), even a modest mean SAP decrease (from 100 to 90 mm Hg) may induce a transient abrupt ICP rise (+30-40 mm Hg), because of the presence of a vicious cycle among CPP, cerebral blood volume, and ICP. In the case of intact autoregulation, PVI shows a mild positive correlation with SAP in the central autoregulation range and a strongly negative correlation below the autoregulation lower limit. In the case of impaired autoregulation, PVI exhibits higher values than in the regulated case, with a mild negative correlation with SAP. CONCLUSION: The present study emphasizes the relevant role of CPP changes, elicited by acute arterial hypotension, in intracranial dynamics. To achieve intracranial stability, CPP should be maintained above 80 to 90 mm Hg. PVI is significantly affected by the active response of cerebral vessels. Hence, it may provide misleading information on craniospinal capacity if it is considered as an autonomous index: rather, it should always be considered together with information on CPP and the status of autoregulation.

Correlations among intracranial pulsatility, intracranial hemodynamics, and transcranial Doppler wave form: literature review and hypothesis for future studies.

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.

Relationships among cerebral perfusion pressure, autoregulation, and transcranial Doppler waveform: a modeling study.

OBJECT: The aim of this study was to analyze how the main values extrapolated from the transcranial Doppler (TCD) waveform (systolic, mean, and diastolic velocity; velocity peak-to-peak amplitude; and pulsatility index [PI]) are affected by changes in intracranial pressure (ICP), systemic arterial pressure (SAP), autoregulation, and intracranial compliance. METHODS: The analysis was performed using a mathematical model of the intracranial dynamics. This model includes a passive middle cerebral artery, the biomechanics of large and small pial arteries subjected to autoregulatory mechanisms, a collapsing venous cerebrovascular bed, the cerebrospinal fluid circulation, and the ICP-volume relationship. The results indicate that there are approximately three distinct zones characterized by different relationships between cerebral perfusion pressure (CPP) and velocity parameters in patients with preserved autoregulation. In the central autoregulatory zone (CPP > 70 mm Hg) the mean velocity does not change with decreasing CPP, whereas the PI and velocity peak-to-peak amplitude increase moderately. In a second zone (CPP between 4045 and 70 mm Hg), in which vasodilation of small pial arteries becomes maximal, the mean velocity starts to decrease, whereas the PI and velocity amplitude continue to increase. In the third zone, in which autoregulation is completely exhausted (CPP < 40 mm Hg), arterioles behave passively, mean velocity and velocity amplitude decline abruptly, and the PI exhibits a disproportionate rise. Moreover, this rise is quite independent of whether CPP is reduced by increasing ICP or reducing mean SAP. In contrast, in patients with defective autoregulation, the mean velocity and velocity amplitude decrease linearly with decreasing CPP, but the PI still increases in a way similar to that observed in patients with preserved autoregulation. CONCLUSIONS: The information contained in the TCD waveform is affected by many factors, including ICP, SAP, autoregulation. and intracranial compliance. Model results indicate that only a comparative analysis of the concomitant changes in ultrasonographic quantities during multimodality monitoring may permit the assessment of several aspects of intracranial dynamics (cerebral blood flow changes, vascular pulsatility, ICP changes, intracranial compliance, CPP, and autoregulation).

An experimental comparison of different methods of measuring wave propagation in viscoelastic tubes.

In this work the values of wave attenuation and phase velocity in a 6 x 9 latex rubber tube closed at the distal end were measured by means of different equations, and varying the distance between transducers. Three equations are based on two simultaneous pressure measurements and on the knowledge of the terminal reflection coefficient (two-point methods). The fourth equation is based on three simultaneous pressure measurements (three-point method). In all cases small amplitude pressure signals (20 mmHg peak-to-peak) were employed. The results of our experiments were then compared with those computed using a classic linear model of wave propagation, and with the high-frequency asymptotic values obtained experimentally using an original method recently developed by the authors. The results obtained with 40 cm between transducers demonstrate that phase velocity (about 15 m/s) and wave attenuation (about 0.003 Neper/cm at 10 Hz) are in agreement with the predictions of classic linear theories in the frequency range 1-15 Hz, provided wall tethering and viscoelasticity are taken into account. Only at certain critical frequencies, which depend on the particular equation employed, does the estimation of wave attenuation become inaccurate owing to an insufficient signal-to-noise ratio. Moreover, wave propagation measurements become inaccurate also at very low frequencies (< 1 Hz). The results obtained using a small distance between transducers (10 cm) demonstrate that the two-point methods maintain greater accuracy than the three-point one. In particular, when reducing the separation between transducers, the three-point attenuation values become 3-4 times greater than the attenuation obtained using the two-point equations. This finding might explain the large differences between propagation values observed in recent in vivo experiments. Finally, asymptotic estimations of the high-frequency phase velocity and attenuation per wave-length turn out rather robust and insensitive to a reduction in the transducer distance. These estimations might, therefore, be usefully adopted during in vivo experiments performed in difficult conditions.

A mathematical model of overall cerebral blood flow regulation in the rat.

In the present work a mathematical model of the cerebrovascular regulatory system in the rat is presented. The model, a generalization of our previous one, includes the reactivity of proximal segments of the cerebrovascular bed and the neurogenic and myogenic feedback regulatory mechanisms besides the action of chemical regulatory factors. The model is then used to analyze the interaction of mechanisms regulating cerebral blood flow in several conditions of physiological importance. In the first stage of the work we simulated experiments in which the neural fibers are cut and artificially stimulated with external means. According to experimental evidence, simulation results point out the existence of an escape of blood flow from stimulation. The model imputes this escape phenomenon to the antagonistic action of chemical factors working on the distal segments of the cerebrovascular bed. In a second stage, we studied the neurogenic mechanism action in a physiological closed-loop condition. With this general model, autoregulation to arterial pressure changes and postischemic reactive hyperemia have been analyzed. A comparison of simulation results with recent experimental data shows that the model is able to produce 60-70% of the experimental regulatory capacity of the cerebrovascular bed. However, some relevant discrepancies still exist between the model and the experimental results, especially as regards the dilatory capacity of small cerebral arterioles. These discrepancies underline the existence of further regulatory mechanisms working on the cerebrovascular bed, the nature of which must still be clarified.

A mathematical model of the carotid baroregulation in pulsating conditions.

A mathematical model of short-term arterial pressure control by the carotid baroreceptors in vagotomized subjects is presented. It includes an elastance variable description of the left and right heart, the systemic and pulmonary circulations, the afferent carotid baroreceptor pathway, a central elaboration unit, and the action of five effector mechanisms. Simulation results suggest that the carotid baroreflex is able to significantly modulate the cardiac function curve, but this effect is masked in vivo by changes in arterial pressure and atrial pressure. During heart pacing, cardiac output increases with frequency at moderate levels of heart rate, then fails to increase further due to a reduction in stroke volume. Shifting from nonpulsatile to pulsatile perfusion of the carotid sinuses decreases the overall baroreflex gain. 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 control is less important. In all cases, there has been satisfactory agreement between model and experimental results.

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 maneuvers, 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).