Dali J. Patel

The Elastic Symmetry of Arterial Segments in Dogs

Elastic symmetry was studied in the middle descending thoracic aorta, abdominal aorta, and left common carotid artery under physiologic ranges of loading in ten dogs. A segment of the blood vessel was isolated and hung vertically. As the segment was pressurized, the radius, length, and the rotation of the lower end of the vessel were measured with respect to the fixed upper end. In addition, the angular displacement of a glass whisker initially placed perpendicularly through the wall was measured. From these data it was possible to calculate the values of shearing strains and elongating strains associated with pressurization and various imposed longitudinal stresses. The values of shearing strain varied from 0.003 to 0.115 over pressure ranges of 3 to 270 cm H2O. In all instances the values of shearing strain were much smaller than the corresponding elongating strains. It was concluded that the vessel has elastic properties that are nearly symmetrical about the planes perpendicular to principal stresses under physiologic loading, i.e., the vessel may be treated as a cylindrically orthotropic tube.

Compressibility of the Arterial Wall

The assumption of incompressibility has often been applied to the analysis of arterial-wall elasticity; however, the supporting evidence has been incomplete. The present study was designed to explore this problem in greater depth by accurately measuring the changes in tissue volume associated with large, induced strains on 11 thoracic aorta segments excised from dogs. The radial, circumferential, and longitudinal stresses were measured as the artery was subjected to an internal pressure and longitudinal stretch greater than those in vivo. From these data it was possible to calculate the hydrostatic stress. The associated changes in volume of the aortic wall tissue were measured with a specially designed apparatus. The greatest volumetric strain (ΔV/V) was 0.00165. The bulk moduli obtained by dividing the hydrostatic stresses by the corresponding volume strains averaged 4.44 × 106 g/cm2. Similar studies were also carried out on the abdominal aorta and the carotid, iliac, and pulmonary arteries. The volumetric strains observed were of the same magnitude. It is concluded that for most practical purposes arteries may be considered incompressible.

Endothelial Nuclear Patterns in the Canine Arterial Tree with Particular Reference to Hemodynamic Events

The objective of the study was (1) to measure systematically the orientation, morphology, and population density of endothelial nuclei of the canine thoracic aorta and its major branches and (2) to obtain evidence in a chronic in vivo preparation that altered flow patterns do indeed change patterns of nuclear orientation. For this purpose, a segment of the descending thoracic aorta was removed, opened longitudinally, and reclosed to form a tube with a new longitudinal axis 90° from the original vessel axis. The new segment was then sutured back in place. The animals were killed at suitable postoperative periods. Endothelial nuclear patterns were studied from en face photomicrographs of preparations stained with Evans blue dye. Results indicated: (1) In uniform vessel segments, e.g., middle and lower descending thoracic aorta, the nuclei were oriented parallel to the axis of the blood vessel, and the ratio of major to minor axes of the nucleus was large. The flow in these regions is known to be stable. (2) Nonaxial, less-ordered nuclear orientation with smaller ratios of major to minor axes were found in entrance regions of many major arteries and in the ascending aorta. (3) In chronic studies in which the flow pattern was altered, the nuclear pattern realigned in the direction of flow within 10 days after surgery.

Relation between pressure and diameter in the ascending aorta of man.

The pressure-diameter relationship in the ascending aorta of man was estimated directly in 10 patients undergoing open-heart surgery. The diameter was measured by means of an electrical strain-gauge caliper sutured to the vessel wall. The lateral intravascular pressure was measured using a 22-gauge needle connected directly to a Statham P23Db strain gauge. The results indicate: (1) a gross similarity between the pressure and diameter curves; (2) the mean value for ratio of change in radius to change in pressure (ΔR/ΔP) was 1.82 × 10−3 cm. per cm. H2O (± S.D. 0.80); (3) the mean value for circumferential extensibility was 0.14 per cent change in radius per cm. H2O (± S.D. 0.06); and (4) the change in cross sectional area during an average cardiac cycle was 11 per cent of the diastolic value.

NONLINEAR ANISOTROPIC ELASTIC PROPERTIES OF THE CANINE AORTA

A nonlinear theory of large elastic deformations of the aortic tissue has been developed. The wall tissue has been considered to be incompressible and curvilinearly orthotropic. The strain energy density function for the tissue is expressed as a polynomial in the circumferential and longitudinal Green-St. Venant strains. Limiting application to states of strains wherein the geometric axes are the principal axes and truncating the energy expression to include terms with highest degrees 2, 3, and 4, three expressions with 3, 7, and 12 constitutive constants are obtained. Results of application of these expressions to data from three series of in vitro and in vivo experiments involving 31 dogs have been presented. Whereas all the three expressions are found to be applicable to various degrees, the third-degree expression for the strain energy density function with seven constitutive constants is particularly recommended for general use.

Application of Heated-Film Velocity and Shear Probes to Hemodynamic Studies

A constant-temperature heated-film anemometer system has been adapted for the detailed study of in-vivo aortic velocity fields. Two types of sensing probes were developed: a velocity probe and a velocity-gradient or fluid shear stress probe. These probes were evaluated for steady and pulsatile flow in rigid circular tubes using both a glycerin-water mixture and blood. Measurements using both devices agreed closely with the values predicted by well established theory. Moreover, the integrated velocity profiles that were measured correlated well with the simultaneously recorded flow values using orifice meter and electromagnetic flowmeter techniques. In-vivo studies were made along the thoracic aortas of anesthetized dogs and pigs. Velocity measurements along the aorta indicated that the velocity profiles are blunt. The flow-pulse forms obtained by the heated-film technique in vivo were also similar in magnitude and contour to those obtained simultaneously from an electromagnetic flowmeter. Fully developed turbulent flow was not observed; however, occasional “eddy” turbulence occurred in the aortic arch of dogs weighing less than 30 kg. Preliminary measurements indicate that peak wall-shear stresses reach values that are approximately one-third that of the endothelial yield stress.

Longitudinal Tethering of Arteries in Dogs

The magnitude and properties of longitudinal vascular tethering were studied in the thoracic aorta, abdominal aorta, and femoral artery of 23 dogs. The tethering was found to consist of a dominant viscoelastic restraining element that demonstrated a moderate degree of stress relaxation and a significant inertial component that was related to the mass of the vessel and its surrounding tissues (the “added mass”). Static and dynamic studies of these properties showed them to be surprisingly linear. The simplest linear model that could simulate these experimental data consisted of two elastic components, two frictional components and a lumped inertial component. Within the physiologic range of frequencies (1 to 20 cycles/sec), the two elastic components became dynamically coupled so that they appeared to act as a single spring, the stiffness of which could be characterized by a “dynamic spring constant.” The mean value of the dynamic spring constant was 12 g/cm3 for the thoracic aorta; it increased along the aorta toward the femoral artery to almost 70 times that value. Contrary to the simple tethering model assumed by Womersley, these data showed that the mechanical behavior of the system is strongly influenced by frictional components.

Static Elastic Properties of the Left Coronary Circumflex Artery and the Common Carotid Artery in Dogs

Static elastic properties were studied in isolated segments of the left coronary circumflex artery (LCCA) and the right common carotid artery (CA) from 14 dogs at in-vivo values of pressure and length. A microscope with a Filar micrometer was used to measure radius and length. From these data it was possible to study the pressure-radius relationship and compute various anisotropic elastic moduli as well as the strain energy density (SED). Results indicate: (1) Both arteries exhibited hysteresis which could be minimized within two inflation-deflation cycles. (2) The pressure-radius relationship at constant length was essentially linear over a pressure range corresponding to the in-vivo pulse pressure. (3) The value of volume distensibility was 3.4 × 10−6 cm2/dyne for LCCA and 1.5 × 10−6 cm2/dyne for CA. (4) LCCA was more distensible than CA in the circumferential direction. (5) LCCA was stiffer in the longitudinal direction than in the circumferential direction; the reverse was true of CA. (6) SED values at physiologic dimensions were 314 × 103 dyne/cm2 for LCCA and 226 × 103 dyne/cm2 for CA. These values could be reproduced within 6% when the loading procedure was altered.

Relationship of Pulmonary Artery-Wedge Pressure to Left Atrial Pressure in Man

The pulmonary artery-wedge and left atrial pressures were recorded simultaneously in 11 patients during a control state, during norepinephrine infusion, as well as during positive and negative intra-alveolar pressures. A good correlation (r = 0.95) found between the two pressures permits the use of corrected pulmonary artery-wedge pressure in calculation of pulmonary vascular resistance under control and test conditions.

Effect of Hypertension on Elasticity and Geometry of Aortic Tissue From Dogs

Inflation-extension experiments were carried out on segments of the descending thoracic aortas from 4 normotensive and 4 hypertensive dogs rendered hypertensive using either unilateral or bilateral renal artery constriction. Intravascular pressures up to 200 mm Hg and axial forces up to 200 g were used. The external diameter of the segment and the distance between two longitudinally spaced gage marks were recorded photographically at each pressure-force level combination. Dimensions in the underformed configuration were measured at the end of the inflation-extension experiment. Data were analyzed for changes in geometry and force-deformation response. Results indicate that: 1. Under sustained hypertension the wall thickness in the underformed configuration increases with a concurrent reduction in the in-situ longitudinal extension ratio. 2. This dual tissue response accomplishes substantial reductions in the circumferential and longitudinal stresses from the levels that would be reached at equivalent pressures in the absence of these geometric changes. 3. At comparable intravascular pressures the extensibility in the circumferential direction is slightly greater for the hypertensive aortas as compared to normals. However, the stress-extension ratio relationship in the circumferential direction is similar in the two groups. 4. The stress-extension ratio relationship in the longitudinal direction indicates that the hypertensive aorta is stiffer than its normotensive counterpart.