Ursino, Mauro, and Carlo Alberto Lodi. A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics. J. Appl. Physiol. 82(4): 1256–1269, 1997.—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.

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.

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.

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