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

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

Background and Purpose Until now the assessment of intracranial pressure (ICP) required invasive methods. The objective of this study was to introduce an approach to a noninvasive assessment of continuous ICP curves.

Methods The intracranial compartment was considered a “black box” system with an input signal, the arterial blood pressure (ABP), and an output signal, the ICP. A so-called weight function described the relationship between ABP and ICP curves. Certain parameters, called transcranial Doppler (TCD) characteristics, were calculated from the cerebral blood flow velocity (FV) and the ABP curves and were used to estimate this weight function. From simultaneously sampled FV, ABP, and (invasively measured) ICP curves of a defined group of patients with severe head injuries, the TCD characteristics and the weight function were computed. Multiple regression analysis revealed a mathematical formula for calculating the weight function from TCD characteristics. This formula was used to generate the ICP simulation. FV, ABP, and ICP recordings from 11 patients (mean age, 46±14 years) with severe head injury were studied. In each patient, ICP was computed by a simulation procedure, generated from the data of the remaining 10 patients. The simulation period was 100 seconds.

Results Corresponding pressure trends with a mean absolute difference of 4.0±1.8 mm Hg between computed and measured ICP were observed. Shapes of pulse and respiratory ICP modulations were clearly predicted.

Conclusions These results demonstrate that this method constitutes a promising step toward a noninvasive ICP prediction that may be clinically applicable under well-defined conditions.

Noninvasive prediction of intracranial pressure curves using transcranial Doppler ultrasonography and blood pressure curves

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. >

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

The goal of this work is to study the cerebral autoregulation, brain gas exchange, and their interaction by means of a mathematical model. We have previously developed a model of the human cardiopu...

https://www.physiology.org/doi/pdf/10.1152/ajpheart.00594.2003

Cerebral autoregulation and gas exchange studied using a human cardiopulmonary model

Our knowledge of cerebrospinal fluid (CSF) hydrodynamics has been considerably improved with the recent introduction of phase-contrast magnetic resonance imaging (phase-contrast MRI), which can provide CSF and blood flow measurements throughout the cardiac cycle. Key temporal and amplitude parameters can be calculated at different sites to elucidate the role played by the various CSF compartments during vascular brain expansion. Most of the models reported in the literature do not take into account CSF oscillation during the cardiac cycle and its kinetic energy impact on the brain. We propose a new lumped-parameter compartmental model of CSF and blood flows in healthy subjects during the cardiac cycle. The system was divided into five submodels representing arterial blood, venous blood, ventricular CSF, cranial subarachnoid space, and spinal subarachnoid space. These submodels are connected by resistances and compliances. The model developed was used to reproduce certain functional characteristics observed in seven healthy volunteers, such as the distribution (amplitude and phase shift) of arterial, venous, and CSF flows. The results show a good agreement between measured and simulated intracranial CSF and blood flows

A New Lumped-Parameter Model of Cerebrospinal Hydrodynamics During the Cardiac Cycle in Healthy Volunteers

An electrical circuit model of the cerebral circulation is presented. Changes of pulsatile waves of the intracranial pressure (ICP) and the cerebral blood volume (CBV) with ICP increment were investigated by simulation of the cerebral blood flow using this model. The simulation is performed by a small signal approximation using the pulsatile component. The results obtained are able to explain the phenomenon of changes in pulsatile wave of ICP with ICP increment. With regard to the CBV, the modeling results are useful for application to rheoencephalography (REG) using electrical impedance method for noninvasive ICP monitoring.

A Simulation Study of Intracranial Pressure Increment Using an Electrical Circuit Model of Cerebral Circulation

A tetrapolar circuit and method using a magnetic field is proposed for measuring the local electric impedance change in living tissue. On the basis of this method, the authors designed an apparatus that can detect impedance changes in two closely situated parts of living tissue, simultaneously and independently. Using this apparatus, they showed the effectiveness of the proposed method by an in vitro experiment and by an in vivo measurement of pulsatile waveforms in the forearm arteries. The detection sensitivity for a local impedance change was confirmed to be higher than that of the conventional tetrapolar method. Pulsatile impedance waveforms measured in the radial and the ulnar parts of the forearm were consistent with those estimated from the anatomical structure. >

New tetrapolar circuit method using magnetic field for measurement of local impedance change in biological substances

Electrical circuit model of cerebral circulation

In order to measure a local impedance of biological substances, a new method of the tetrapolar circuit in combination with eddy current is proposed. In this method, current distribution can be restricted to the desired part and errors due to electrode impedance uncertainty can be also eliminated because of using the tetrapolar technique. Therefore, this method would be useful to expand the application area of impedance measurement in physiological studies.

New Method of Tetrapolar Circuit in Combination with Eddy Current for Impedance Measurement of Biological Substances

An electronic circuit model of the coronary vessel using field effect transistor (FET) was used to perform dynamic simulation of the left coronary circulation and to study the changes in the endo-epi flow ratio of the myocardium in order to demonstrate the vulnerability of the subendocardial layer of the intramyocardium to various coronary arterial diseases and the way the coronary arterial blood flow is effected by the occurrence of abnormality in the heart. Under normal condition, the simulated endo-epi flow ratio was found to be 0.68. The changes in the flow ratio were observed while varying the septal arterial resistance, mean arterial pressure and intramyocardial pressure individually. The mean flow in the subendocardium was found to decrease at a rate faster than that in the subepicardium with the increase in the septal arterial resistance and the intramyocardial pressure. The same tendency was also observed while the arterial pressure was lowered. From all these observations, it can be concluded that the subendocardium is more vulnerable to ischemic heart diseases than the subepicardium.

Study of the endo-epi flow ratio by using an electronic circuit model of the coronary vessel

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