• The problems of characterizing pulsatile patterns of pressure and flow in the arterial system are intriguing and complex. Ejection of blood from the left ventricle initiates nonlinear transients in pressure and flow at the root of the aorta. These transients initiate complex pulse patterns that are propagated throughout the arterial tree. Some of the factors that must be reckoned with in an analysis of these patterns are itemized in the list that follows: 1) The force initiating the transients is itself complex; the velocity of ventricular ejection increases rapidly with the opening of the aortic valve, then declines slowly to reach a negative nadir with the closure of the aortic valve.2) The distensibility of the walls of the arteries receiving this positive increment of pressure and flow has an important influence on pulse patterns. This physical property of the arterial wall is also responsible for changes in configuration and velocity of the transients as they pass over the arterial tree. The pulsatile patterns are further distorted by 3) frictional losses of energy with both positive and negative flow of the blood, and by the 4) branching and tapering architecture of the arterial tree. 5) The resistances to forward motion of blood through the distal arteriolar beds also have their effects on the contours of the arterial pulses observed upstream.From the Departments of Civil Engineering, Surgery and Physiology, University of Michigan, Ann Arbor, Michigan.Supported in part by the National Institutes of Health, U. S. Public Health Service through project Xo. HE07443-01.The experimental work was completed while Dr. Keitzer was supported in part by projects B-2290C1 and H-4260C3 from the U. S. Public Health Service and the Veterans Administration Hospital, Ann Arbor, Michigan.Received for publication February 25, 1963. Both experimental and theoretical methods have been used to analyze and to quantify the influence of these factors on the arterial pulse pattern. The experimental approach has profited substantially from new instrumentation which permits a recording of the transients of both pressure and flow with a high degree of fidelity at various levels of the arterial tree. "4 The theoretical approach employs established mathematical relations between known physical parameters which permit the prediction of pressure and flow at specific points in the arterial tree and specific times in the cardiac cycle. If an adequate mathematical expression were available to describe these relations, the fit of these predictions to the actual measured values would then become a valuable tool both for assessing the accuracy of the selected values for the physical parameters and for evaluating the significance of the various factors that influence these transients in the arterial tree.The theoretical analysis of these transients then has two requirements: 1) realistic values for factors that influence the transients, and 2) a mathematical statement of the interrelationship of these factors which will define pressure and ...
Besides the well-known earlier methods of rotating-disk calculations such as those developed by Grammel and others, an extensive treatment is given of more recently developed procedures including difference methods and those which involve the division of the disk profile into a number of conical-shaped segments, which are then fitted together. Since the author limits himself mainly to elastic conditions, very little information is given on such important practical subjects as the effects of plastic flow, creep, and fracture. In spite of this limitation, the book nevertheless should be of considerable interest and value to research men and designers.
The calculation of transient flows and pressures in a gas network by the cbaracterr"sticsmethod has a time interval restricted to the shortest pipe length divided by the isotbennal wave speed. To avoid tb is restriction, the centered implicitdifference method is developed. lt requires two equations for each pipe and one equation for each junction. The Newton-Rapbson method of handling the nonlinear equations is utilized and sparse matrix algebra reduces the time of solution of the simultaneous equations. An example is presented wbicb compares results btc'.ned .,,; +A w.',, & implicit scheme with results obtained from the characteristics method of solving jor conditions at each node in turn. The new method is then applied to a simplified grid of the Consumers Power Co. and a comparison is made with field measurements.
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