RHEOLOGIC PROPERTIES OF BLOOD VESSELS 
Joseph S. Janicki,* Dali J. Patel,** John T. Young" and Ramesh N. Vaishnav*** 
The blood vessels under consideration were the mid- 
dle descending thoracic aorta (MDTA), the left cir- 
cumflex coronary artery (LCCA) and the carotid artery 
(CA). Several assumptions concerning these vessels 
were necessary before the rheological properties could be 
determined. They are (1) homogeneity (uniform me- 
chanical properties over a vessel length of 2 to 8 cm 
depending on the vessel studied) ; (2) cylindricity (no 
vessel taper and a circular cross section) ; (3) thin- 
walled (ratio of mid-wall radius to thickness is 10 or 
larger) ; (4) incompressibility (wall volume remains 
constant when subjected to large deformations) ; and 
(5) curvilinear orthotrophy (elastic symmetry about 
the planes perpendicular to the radial, circumferential 
and longitudinal directions). Under these assumptions, 
constitutive relations were developed whereby the static 
and dynamic, incremental, anisotropic moduli could be 
calculated from pressure, diameter, longitudinal force, 
length and wall volume measurements. In 14 dogs the 
static elastic properties of the LCCA and the CA were 
determined in vitro and in 14 other dogs the static 
elastic properties of the MDTA were studied in vivo 
and in vitro. Results indicate (1) both the LCCA 
and MDTA were more distensible than CA in the cir- 
cumferential direction; (2) the LCCA was stiff er in 
the longitudinal direction than in the circumferential 
direction; the reverse was true of the CA; and (3) the 
elastic moduli of the MDTA increased with an increase 
in intravascular pressure. In 10 additional dogs the 
visco-elastic properties of the MDTA were also studied 
in vivo over the frequency range of 0 to 5 hertz. Re- 
sults indicate (1) the longitudinal visco-elastic modulus 
to be the largest; (2) the storage moduli, in all direc- 
tions, increased initially with frequency and then essen- 
tially remained constant; and (3) the loss moduli, in 
all directions, did not significantly change with fre- 
quency. 
INTRODUCTION 
The need to quantify the mechanical proper- 
ties of blood vessels has long been recognized 
as a fundamental aspect of the understanding 
of cardiovascular hemodynamics. For example, 
* Department of Medicine, University of Alabama, Birmingham, 
Alabama. 
** Section on Experimental Atherosclerosis, National Heart and 
Lung Institute, N. I. H., Bethesda, Maryland. 
**♦ Department of Civil and Mechanical Engineering, The Catholic 
University of America, Washington, D. C. 
knovi^ledge of blood vessel rheology is necessary 
(1) in the design of vascular prosthesis and 
heart assist devices, (2) in the interpretation 
of hemodynamic data for diagnostic or thera- 
peutic purposes, and (3) in the understanding 
of degenerative vascular diseases. 
One of our primary objectives over the past 
ten years has been the development of an ex- 
perimental technique vi^hich enabled us to meas- 
ure the rheologic properties of blood vessels in 
the living dog. This technique required the 
adaptation of several basic engineering con- 
cepts to the biological system. In doing this, 
several simplifying assumptions had to be made 
in order to keep the mathematics tractable. 
Whenever possible, these assumptions were vali- 
dated experimentally. Also, special instrumenta- 
tion had to be designed and fabricated. To date, 
the canine middle descending thoracic aorta 
(MDTA) has been studied both dynamically 
and statically m vivo and in vitro, and in addi- 
tion, the left circumflex coronary artery (LCCA) 
and the carotid artery (CA) have been studied 
statically in vitro. It is the purpose of this 
article to review this technique and the experi- 
mental results so obtained. 
THEORY 
This section condenses the extensive review 
given by Patel and Vaishnav.^ 
The blood vessel segment is taken to be a 
thin-walled circular cylindrical tube of con- 
stant thickness. At a given state of initial strain, 
the vessel wall is considered linearly elastic 
and curvilinearly orthotropic. The arterial tis- 
sue is assumed to be homogeneous and incom- 
pressible. The implication in assuming the ves- 
sel to be thin-walled is that the distribution of 
the circumferential stress across the thickness 
will be uniform. In engineering practice this 
assumption is made when the ratio of mid-wall 
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