Fourier analysis of the cerebrovascular system.

Abstract

We performed Fourier analysis of the middle cerebral artery blood flow velocity waveform envelope in 14 normal subjects (group A) and 15 patients, of whom five had arteriovenous malformations (group B), five had cerebral vasospasm (group C), and five had arterial hypertension (group D). Measurements were obtained under conditions of normocapnia, hypercapnia, and hypocapnia. The Fourier coefficients measured in the first five harmonics of the Doppler waveforms of group A were used as the reference baseline and were compared with the coefficients found in the other three groups. Group B showed significantly lower Fourier coefficients, while groups C and D showed higher coefficients (p<0.05). The elevation of the Fourier coefficients occurred in an alternating pattern in group C and a decremental pattern in group D. This distinction was attributed to possible differences in the underlying pathophysiological processes. The degree of vascular distensibility of the cerebral arterioles, inferred from the shape of the Fourier analysis curves, was compared in all four groups. Vascular distensibility was characterized as abnormal in arteriovenous malformations, vasospasm, and arterial hypertension. Fourier coefficients may be better indicators of cerebrovascular abnormalities than mean blood flow velocity in hypertension and pulsatUity index in arteriovenous malformations, vasospasm, and hypertension. (Stroke 1991^2:721-726)

Fourier Analysis of the Envelope of the Ophthalmic Artery Blood Flow Velocity

“…4 Fourier analysis of the middle cerebral artery considered changes of the single sinus waves from the mean value but did not define the ratio of the most powerful harmonics over age, in contrast to our proceeding. Nevertheless, the results revealed that the amplitude of the respective harmonic divided by the mean value of the blood flow velocity particularly of the first 3 harmonics was increased in patients with hypertension as compared with healthy control subjects.…”

“…SC and SI were not under the control of MAP in men but were in women (SC: 11.2%, Pϭ0.001; SI: 13.1%, PϽ0.001). In contrast to the equation for men, 4 the resulting equation for women 5 additionally included the MAP. (4) SIϭ0.84Ϫ0.008ϫage…”

“…15 Experimental data indicate that aging alters endotheliumdependent relaxation in arteries, 16 and loss of the oscillatory waveform represents an early and consistent finding with aging and hypertension. 4,17 Different frequency fractions of the envelope waveform of the blood flow velocity possess different input resistances, meaning that individual oscillations of the harmonic content are exposed to different wave resistances, which are induced by both the peripheral reflexions and the vessel elasticity. 18 In this context, the power of the first 5 harmonics Ͻ10 Hz is well known 19 and, therefore, was used for further considerations.…”

“…The fast Fourier transform represents a mathematical approach for analysis, which is an optimized and refined algorithm 3 based on the discrete Fourier transform. Respective examinations were performed in the cerebrovascular system, 4 in the cardiovascular and respiratory system, 5 and in other different vessel areas to measure the input impedance. 6,7 Fourier coefficients of the first to tenth harmonic oscillation have been shown to differentiate between normal and pathological vessels, 8 and already in small retinal vessels of young patients with arterial hypertension, the hemodynamics was shown impaired.…”

Cold stimulation induces different responses of ophthalmic artery blood flow velocity depending on baseline blood pressure and gender

“…8 With aging and in arterial hypertension, the oscillatory waveforms disappear early. 9,10 The cold pressor test (CPT) is a well-standardized stress test to determine the integrity of the autonomic nerve system. Cold stimulation of a peripheric part of the body is followed by a global sympathetic activation, 11 which leads to a significant arteriolar vasoconstriction with increased blood pressure, and depending on test conditions with 3 or without 12,13 changes of the heart rate.…”