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.

Abstract: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 28:143-157, 2007.

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.

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.

Several cardiovascular and pulmonary models have been proposed in the last few decades. However, very few have addressed the interactions between these two systems. Our group has developed an integrated cardiopulmonary model (CP Model) that mathematically describes the interactions between the cardiovascular and respiratory systems, along with their main short-term control mechanisms. The model has been compared with human and animal data taken from published literature. Due to the volume of the work, the paper is divided in two parts. The present paper is on model development and normophysiology, whereas the second is on the model's validation on hypoxic and hypercapnic conditions. The CP Model incorporates cardiovascular circulation, respiratory mechanics, tissue and alveolar gas exchange, as well as short-term neural control mechanisms acting on both the cardiovascular and the respiratory functions. The model is able to simulate physiological variables typically observed in adult humans under normal and pathological conditions and to explain the underlying mechanisms and dynamics.