Mammalian hemodynamics: a new similarity principle.
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Biomedical subjects
Publications and source records attributed to A Noordergraaf.
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Under rest conditions, changes in the Korotkoff sounds at phases I, IV, and V can be correlated with specific frequencies within the bandpass of the stethoscope. A filter capable of detecting the changes in Korotkoff sounds at phases I, IV, and V is described together with the frequency changes that characterize these phases. The importance of frequency components outside the bandpass of the stethoscope is stressed, especially in terms of the possibility of yielding more clinical information and, perhaps, additional clues above the origin of the Korotkoff sounds themselves.
When considering the use of Fourier series in hemodynamics, the question is whether one can relate the frequency components of the flow oscillations to the corresponding ones of pressure using impedance concepts. For the arteries, this method provided the basis for great advances in understanding. However, it is precisely because the arterial tree acts almost linearly while its properties do not change markedly within one beat that frequency analysis achieved such success. For the ventricle, in which the mechanical properties vary widely over the course of one heart cycle, Fourier analysis loses its usefulness. Consequently, we must return to the time domain for formulating a description of the heart as a pump. A time-domain method, the impulse response, is suggested as a possible alternative to impedance.
The performance of catheter-manometer systems for the measurement of pulsatile pressure has been evaluated by both experimental techniques and theoretical considerations. The former approach has shown, on occasion, multiple maxima in the amplitude response. The latter has been approached in a variety of ways, ranging from extreme lumping to application of transmission line theory while employing different configurations in the system's representation. Multiple maxima have also been seen, The present paper identifies the sources of the differences found and compares the relative merits of various theoretical approaches. It introduces the compliance of the system as a figure of merit and provides a simple first-order approximation formula for evaluation of the quality of a system. Damping and impedance matching to improve the system's frequency response were studied. It was found that they were not needed in a very stiff or a very compliant system, nor should one worry about the representation of such a system.
Three dimensional laminar, viscid flow is developed for Newtonian fluids which provides absolute values for axial, radial and tangential velocity fields everywhere if the dimensions of the vessel are known and two simultaneous axial velocities e.g. on and off the central axis in the same plane, and the central axis velocity gradient are measured. In addition, normal and shear stresses are determinable. The equation set satisfies gemoetric and other known flow limiting conditions such as no slip at surfaces etc. and are amenable for inclusion in general, dynamic flow expressions. Alternatively they may be used alone for certain problems involving gradients and secondary flows. A range of illustrations are shown for a distorting vessel with elliptic cross-section and small axial taper (analogous to the pulmonary trunk during ejection).
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A new and simple method is presented that is suitable for the fabrication of inflatable cuffs for any gross vascular size. The method lends itself to mass production which is particularly useful for the fabrication of small cuffs. The procedure generally consists of spraying latex on a rotating cylinder in two separable layers. An activating tube is inserted between the layers and the edges sealed. Outward expansion is prevented by means of a suitable backing material.
Experiments designed to examine the relationship between electrical and mechanical events in voluntarily contracting human muscle were performed. Experiments reported in the literature, as well as our own, were categorized according to technique into one of four types: (1) isometric-isotonic, (2) isometric-anisotonic,(3) anisometric-isotonic or (4) anisometric-anisotonic. A general relationship between the absolute value of the surface electromyogram (the absolute value of E and the force (F) generated by the contraction is proposed. This is the integral of the absolute value of E dt = k-1integralF dx i-2integralF dt, where k-1 and k-2 are constants. In the isometric-isotonic condition, this equation reduces to a linear relation between the average electromyogram and the force of contraction. A quadratic relation exists in the isometric-anisotonic, constantly increasing contraction, between the integrated electromyogram and the force of contraction. Also, this equation predicts linear relations for anisometric-isotonic contractions, and quadratic relations for an accelerated rate of contraction, between the average electromyogram and force of contraction. Both the data reported in the literature and our data provide confirmatory evidence for the unifying theory offered in this paper.
The dynamic local distensibility of the abdominal aorta was measured in 11 anesthetized dogs by recording simultaneously phasic pressure and instantaneous intravascular cross-sectional area, utilizing a special transducer. Axial motion of the vessel wall was recorded using a modification of the same transducer. A nonlinear relationship was found to exist between area and pressure in most cases studied. Fourier analysis was performed on data from eight experiments in order to obtain frequency characteristics of distensibility. In roughly half of the cases, Fourier analysis revealed that pressure variations displayed a phase lead over area variations for frequencies up to 10 Hz. This phenomenon was ascribed to viscoelastic properties of the vessel wall and the magnitude of the phase leads roughly matched those found in vitro by others. The behavior of the vessel wall in these instances was correctly predicted by the dynamic formula for distensibility, derived by others from wave transmission theory in which absence of axial wall motion is assumed. In these experiments, axial motion of the wall was found to be virtually absent. In the other half of the cases, the reverse situation was obtained: a phase lead of area variations over pressure variations for frequencies up to 15 Hz. In those cases a craniocaudal axial displacement of the vessel wall was observed with each systole, amounting to around 1 mm. The finding of the phase leads was partially explained by a dynamic formula for distensibility, developed by us from the theory of wave transmission in which free axial motion of the wall is a chosen boundary condition. The sign and order of magnitude of the phase leads were correctly predicted by the theoretical formula, but there was a disagreement on the frequency range in which they occurred. We concluded that additional forces, not yet considered in theoretical treatments, are operative on the aortic wall, which account for this lack of agreement. The frequency dependent properties of distensibility in vivo cannot be compared to those obtained in vitro in those cases in which there is axial displacement of the vessel wall of the same order of magnitude as the radial extensions.
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