The media of 14 regions of the aorta and 3 regions of the pulmonary artery of dogs were subjected to a step-function circumferential stretch taking 20 msec to complete. The tension rose synchronously with the increase in circumference, then dropped exponentially to a reasonably steady state within 2 sec. A mathematical model, developed consistent with this stress-relaxation curve, showed how to use the tension curves to measure a viscous, a serieselastic, and a parallel-elastic constant unique for a given curve. These constants were compared with the microscopic structure of the same or similar segments; collagen was determined as hydroxyproline in a water soluble fraction, elastin as hydroxyproline in the residue and from the width and number of elastic lamellae, and muscle from the nitrogen content of a nonfibrous fraction, from cell counts and from contractility. The constituents varied widely and independently enough to permit correlating viscous and elastic constants with microscopic structure. The viscous and series-elastic constants were higher where muscle content was high, and increased markedly when the muscle was tonically contracted. The parallel-elastic constant was high when elastin was high and in the presence of contracted muscle, but seemed independent of collagen content, at the moderate tensions tested.

The media of eight regions of the aorta and three of the pulmonary artery of dogs, as well as isolated elastin, collagen, and smooth muscle obtained from vascular and other sources, were subjected to a step-function circumferential stretch at a variety of temperatures between 0° and 70°C. The tension rose to a peak synchronously with the stretch and then fell along an essentially exponential course to a steady tension. Suitable use of the peak tension, the steady-state tension, and the time required to go from peak to steady state, supplied three temperature-dependent parameters (one viscous and two elastic) characteristic of the material. The two crystalline polymers, collagen and smooth muscle, had higher constants at low temperatures, and the amorphous polymer, elastin, had higher constants at high temperatures. Collagen differed from smooth muscle in its inertness to autonomic drugs and in its elastic modulus. Intact arteries stretched slightly (2% to 20%) in the presence of phenylephrine behaved like smooth muscle; arteries stretched more (20% to 70%) behaved like elastin. At both strain levels, the tensions developed were compatible with in vivo pressures. Arteries stretched even more (> 100%), to tensions compatible with pressures of 300 mm Hg, behaved like collagen.

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Nine aortas from recently killed dogs were sectioned into 21 or more ring segments supported horizontally on two hooks in Ringer's solution. One hook oscillated sinusoidally from .01 to 21 Hz to stretch the segments 1.2% in excess of 4 or more mean strain levels from 5 to 100%. The segments were kept at 4 temperature levels (0°, 20°, 37°, 60°C). The other hook was coupled to a force transducer. At frequencies below 1 Hz, the force registered was sinusoidal with the same frequency as the stretch which it led, unless the specimen contained demonstrably contracted smooth muscle; then the stress was nonlinear and lagged behind the strain at frequencies below .05 Hz. As frequencies rose above 1 Hz, the force amplitude rose to a maximum, resonating at frequency co r , which was higher at higher initial strains. Concurrently the phase shift increased to 90° at another frequency co^. When go > O) r , viscous losses were appreciable, in agreement with other measurements and implicating either muscle or elastin. These two wall components could be distinguished from each other by responses to drugs and to changes in temperature. Absolute dynamic modulus, storage modulus, loss modulus, phase shift, and loss angle measured from stress-strain loops compared favorably with similar measurements published for other visco-elastic materials and with viscous and elastic constants obtained from stress-relaxation experiments on aorta. • Visco-elastic constants already obtained from step-function-induced stress-relaxation curves (1, 2) are theoretically sufficient (3) to permit predictions of the responses to other forcings (4-6). ADDITIONAL KEY WORDSStep-function forcings have not been adequate, however, for determining whether stress-relaxation can be described correctly by an exponential curve with a single time constant (7) nor for obtaining the total This investigation was supported in part by U. S. Public Health Service Grant GM-14659-01 from the National Institutes of Health.Accepted for publication January 11, 1968. value of an elastic constant which is related to the loss modulus (1). It is not clear whether this difficulty derives from material properties or from the fact that a true stepfunction stretch or release is not realizable, since it takes a finite amount of time to go from one length to another. This question can be settled only with sinusoidal forcings which span frequencies far below resonance (viscoelastic region) or are demonstrably in the resonance region. The present work succeeded in inducing sinusoidal circumferential stretch of arteries at frequencies from .01 to 21 Hz which spanned the visco-elastic as well as resonance behavior. Suitable measurements were taken