JOSEPH S. JANICKI, DALI J. PATEL, JOHN T. YOUNG AND RAMESH N. VAISHNAV 
581 
value of the elastic moduli in the third group 
were always higher (p <0.01) than in the first 
group, and (2) in general E2>Ee>Er for in vivo 
physiologic strain states. This indicates that 
the MDTA exhibits an anisotropic behavior in 
vivo. 
Typical results from a dynamic, in vivo study 
are given in Table II. The vessel was evaluated 
around a mean pressure of 140 cm HoO and 
around an initial state of strain given by kg = 
1.41 and = 1.62. The following points are 
noteworthy: (1) the longitudinal viscoelastic 
modulus is the largest; (2) the values of E^, E^ 
and Er increase initially with frequently (0 to 2 
hertz) and then essentially remain constant; 
and (3) E^ , EJ and E^ are much greater 
than E" , E" and E" . 
It should be reemphasized that the above re- 
sults are valid only around the given physiologi- 
cal states of strain, and any other state of strain 
will require a different characterization of the 
vessel properties. Thus, when comparing data 
from various sources, one should always be cer- 
tain of where on the large, nonlinear, stress- 
strain curve the data were obtained. A non- 
linear theory for large elastic deformation, 
which in effect removes this restriction, has re- 
cently been developed.® This theory provides (1) 
a constitutive relation relating the stresses in 
an artery directly with the state of initial strain 
and (2) the values of the incremental moduli 
around any state of large strain. However, un- 
der its present stage of development, the visco- 
elastic (dynamic) case has not been incorpo- 
rated. Applying this theory to the static in vivo 
MDTA data resulted in agreement within 10% 
Table II. — Typical, Viscoelastic Results from the 
Canine Middle Descending Thoracic Aorta 
Fre- 
quency 
(Hz) 
E6 
cnri 
E« 
(dynes/ 
= X 10«) 
Ee 
cm 
(dynes/ 
2 X lOf ) 
Er 
cm 
Er 
(dynes/ 
= X 10«) 
0 
6.12 
0 
9.51 
0 
5.07 
0 
0.5 
6.87 
0.09 
14.38 
1.80 
5.49 
0.41 
1.0 
6.91 
0.07 
14.78 
1.70 
5.59 
0.41 
2.0 
6.91 
0.20 
15.23 
1.30 
5.66 
0.22 
3.0 
7.08 
0.08 
15.09 
2.49 
5.80 
0.60 
4.0 
7.15 
0.13 
15.05 
1.86 
5.81 
0.46 
5.0 
6.96 
0.02 
14.66 
2.44 
6.19 
0.66 
Ee, Ez and Er are the complex incremental viscoelastic moduli in 
the $, z and r directions; Ee, Ez and Er are the real parts of the 
complex moduli representing the elastic coefficients and Eo, Ez, and 
Er are the imaginary parts related to the viscous coefficients. 
for Eg and E^ and 16% for E^. Furthermore, in 
a set of in vitro experiments in which measure- 
ments were made over a wider range of strains, 
the agreement was within 7% for all three 
moduli. 
SUMMARY 
We have developed an experimental tech- 
nique which permits the quantification of the 
anisotropic, viscoelastic behavior of blood ves- 
sels in vivo. Most of the assumptions inherent 
to this technique have been experimentally 
justified. The viscoelastic properties of the 
MDTA and the elastic properties of LCCA and 
CA have been evaluated around a physiologic 
state of strain. 
ACKNOWLEDGMENTS 
We are grateful to Dr. D. L. Fry for his help 
and criticisms throughout this research. We 
thank Dr. T. E. Carew for his collaboration; 
Mrs. V. M. Fry for technical illustrations; 
Messrs. J. M. Pearce, F. Plowman, L. Brown 
and G. Johnson for technical assistance; Mrs. 
C. Floyd for data analysis; and Miss S. Green 
for editing and typing this manuscript. We 
also thank the American Heart Association, 
Inc., for permission to reproduce illustrations 
from previous publications. 
REFERENCES 
1. Patel, D. J. and Vaishnav, R. N. "Rheology of large 
blood vessels." Cardiovascular Fluid Mechanics. In 
press, Academic Press, London, 1972. 
2. McDonald, D. A. Blood Flow in Arteries. Williams 
& Wilkins Co., Baltimore, 1960. 
3. Patel, D. J. and Fry, D. L. The elastic symmetry 
of arterial segments in dogs. Cicr. Res. 24:1, 1969. 
4. Carew, T. E., Vaishnav, R. N. and Patel, D. J. 
Compressibility of arterial wall. Circ. Res. 23:61, 
1968. 
5. Patel, D. J., Janicki, J. S. and Carew, T. E. Static 
anisotropic elastic properties of the aorta in living 
dogs. Circ. Res. 25:765, 1969. 
6. Patel, D. J. and Janicki, J. S. Static elastic prop- 
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common carotid artery in dogs. Circ. Res. 27:149, 
1970. 
7. Patel, D. J. and Fry, D. L. Longitudinal tethering 
of arteries in dogs. Circ. Res., 19:1011, 1966. 
