Systems analysis of cerebrovascular pressure transmission: an observational study in head-injured patients

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✓ In an observational study in head-injured patients, cerebrovascular pressure transmission was investigated using a systems analysis approach whereby the blood pressure (BP) waveform was used as a measure of an input stimulus to the cerebrovascular bed (CVB) and the intracranial pressure (ICP) waveform as the response to that stimulus. The transfer function is a measure of how much pressure is transmitted through the CVB at a given frequency and is calculated using Fourier analysis of the pressure waveforms. The transfer function allows quantification of the pressure transmission performance of the CVB, thus providing a basis for comparison between normal and abnormal function.

Fifteen hundred samples of ICP and BP waveforms were collected from 30 head-injured patients via microcomputer. Off-line spectral analysis of the waveform database revealed four main classes of transfer function: those with an overall flat transfer function (curve type 1); those with an elevated low-frequency response (curve type 2); those with an elevated high-frequency response (curve type 3); and those exhibiting both an elevated low- and high-frequency response (curve type 4). Curve types 2 and 4 were most often associated with raised ICP (> 20 mm Hg), whereas curve types 1 and 3 were most often affiliated with ICP less than 15 mm Hg. Studies of this type may provide insight into the pathophysiology of the CVB and ultimately aid in the prediction and treatment of raised ICP.

Article Information

Address reprint requests to: J. Douglas Miller, M.D., F.R.C.S., Department of Clinical Neurosciences, Western General Hospital, Crewe Road South, Edinburgh EH4 2XU, Scotland.

© AANS, except where prohibited by US copyright law.

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Figures

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    Systems analysis approach in which the blood pressure (BP) and intracranial pressure (ICP) waveforms (f(t) and g(t), respectively) are used as input and output functions to the cerebrovascular bed (CVB). These pressure waveforms can be transformed from the time domain (g(t)) to the frequency domain (G(ω)) through Fourier transformation. Fourier analysis can represent a pressure waveform, as seen in the amplitude spectra, as a series of simpler sine waves consisting of a fundamental component frequency related to the heart rate and a series of higher harmonics at multiples of the fundamental component frequency. The system transfer function (H(ω)), which consists of both amplitude and phase components, describes how the stimulus signals are transformed by the system into response signals and is calculated as the ratio of ICP and BP amplitude and phase values, taken from the amplitude spectra, at each of the measured cardiac component harmonics.

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    Graphs depicting four classes of amplitude transfer function for the first six cardiac component harmonics, based on Fourier analysis of 100 pilot samples from a database of intracranial pressure and blood pressure waveforms collected from 30 head-injured patients. The amplitude transfer functions were calculated and found to cluster into four curve types: 1) those with an overall flat amplitude transfer function, 2) those with an elevated low-frequency response, 3) those with an elevated high-frequency response, and 4) those exhibiting both an elevated low- and high-frequency response.

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    Graphs showing the results of Fourier analysis of the 1400 post-pilot samples from a database of intracranial pressure and blood pressure waveforms collected from 30 head-injured patients, and the amplitude transfer functions prospectively coded into one of four curve types (see legend to Fig. 2 for classification criteria). Data were averaged by amplitude transfer function curve type: curve type 1 = 382 samples, curve type 2 = 243, curve type 3 = 545, and curve type 4 = 202.

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    Graphs showing the results of Fourier analysis of the 1400 post-pilot samples from a database of intracranial pressure and blood pressure waveforms collected from 30 head-injured patients and the phase transfer function data, averaged and classified by amplitude transfer function curve type (see legend to Fig. 2 for classification criteria). The first harmonic phase for curve type 3 shows a positive phase shift compared to the other curve types. Also associated particularly with phase transfer function curve type 3 is the presence of a phase cross-over from a positive to a negative phase. This phase cross-over was not seen with phase transfer function curve type 1. Phase transfer function is expressed in radians.

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    Plot of the coefficient of variation calculated for each of the first eight cardiac component harmonics from the amplitude and phase transfer functions obtained from 30 sequential samples of intracranial pressure and blood pressure waveforms recorded in a head-injured patient in stable condition. The first five harmonics of the amplitude transfer function data (closed circles) show a coefficient of variation less than 10%, the sixth and seventh show a variation of between 20% and 30%, and the eighth harmonic shows a variation of greater than 45%. With the phase transfer function data (open circles), only the first harmonic shows a coefficient of variation of less than 20%.

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    Left: Schematic drawing modeling the cerebrovascular bed as a single elastic tube in which the terminal portions of the tube have an impedance large enough to be considered completely closed, resulting in no flow from the end and a pressure pulse that is fully reflected back toward the input of the tube. In view of the pressure, with respect to time, at three distances (A, B, and C) along the length of the tube, reflection can lead to the formation of a standing wave pattern where, at repeated fixed distances along the tube (distance C), incident and reflected pressure waves coincide resulting in addition, which is measured as an amplification of the pressure pulse at that point. Right: A standing wave pattern is set up where, at each distance along the length of the tube where incident and reflected pulse waves coincide, a peak occurs in the amplitude transfer function and the phase transfer function demonstrates a phase cross-over. The frequency with which the incident and reflected pressure waves coincide is termed the “resonant frequency” and is determined by the physical characteristics of the tube. (Figure adapted from Taylor MG: An introduction to some recent developments in arterial haemodynamics. Aust Ann Med 15:71–86, 1966.)

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