JOSEPH S. JANICKI, DALI J. PATEL, JOHN T. YOUNG AND RAMESH N. VAISHNAV 
579 
the theoretical requirement of two strain states, 
the basic experiment consisted of two parts : (1) 
Variable length-constant volume (i.e., pre- 
dominantly a longitudinal strain state) ; and 
(2) Constant length-variable volume (i.e., pre- 
dominantly a circumferential strain state). Ex- 
perimentally, Part 1 was accomplished by vary- 
ing the length an amount aL, either statically 
or dynamically, around its initial value L and 
recording the resulting change in pressure 
(Ap), external radius (ARe) and force (aF), 
while keeping the volume constant ; and Part 2 
consisted of varying the volume, statically or 
dynamically, and again recording Ap, ARe and 
aF, while keeping the length constant. When 
doing a static experiment, stress-relaxation, fol- 
lowing a perturbation, was allowed to occur by 
waiting one minute prior to data collection. In 
the dynamic experiments, data were recorded at 
6 frequencies — 0.5, 1, 2, 3, 4 and 5 hertz. 
At the end of the experiment, the blood ves- 
sel segment was slit open longitudinally and the 
unstressed length (Lq) and circumference were 
measured. The value of the unstressed radius 
(Ro) was obtained by dividing the value of un- 
stressed circumference by Itt. The wall volume, 
V, was then obtained by either weighing the 
specimen (LCCA and CA) and dividing by 
tissue density (1.06 g/cm^) or determining the 
specimen's (MDTA) loss of weight when sus- 
pended in distilled water. Since the material is 
incompressible, V was a constant and the value 
of thickness, h, was calculated for different 
values of Rp and L from 
equations (6), (8) and (9) have been obtained. 
These quantities were calculated for both strain 
states and substituted into equations (23) and 
(24). The resulting system of four equations 
in three unknowns was then solved using a 
method of least squares. Finally, the solution, 
Cij (i = j = r, Q, z), was converted into incre- 
mental moduli using equations (26). 
RESULTS AND DISCUSSION 
The static in vitro results for the MDTA, 
LCCA and CA are summarized in Table I. It 
is important to point out that the elastic moduli 
given for LCCA and CA are considered to be 
approximate for the following reasons: (1) the 
R 
LCCA ratio ^ is small and could introduce er- 
h 
rors in the calculation of wall stress based on 
thin-wall theory; (2) the computations are sen- 
sitive to error in the measurement of radius and 
to errors due to the inability to keep length 
exactly constant during the variable volume- 
constant length part of the experiment; and 
(3) the measurement of wall volume of these 
segments is very difficult and consequently leads 
to errors in the calculation of wall thickness. 
These considerations would account for the 
large scatter in the elastic moduli values. 
In spite of these reservations, it is reasonable 
to conclude the following: (1) both LCCA and 
CA Jexnonstrate anisotropic behavior in the 
physiologic range; (2) both the MDTA and 
LCCA are more distensible than the CA in the 
circumferential direction; (3) the LCCA is 
h=:Re- 
(27) 
The quantity was then subtracted from the 
measured external radius to obtain the corre- 
sponding mid-wall radius, R. 
The dynamic data, which were recorded on 
analog tape, were digitized at a rate of 500 
samples/second. Then, for each frequency, these 
data were subjected to Fourier analysis, 
whereby the phase angles ^, a and i// were ob- 
tained. Thus, it is seen that all of the data re- 
quired to calculate either the static or dynamic 
incremental strains and stresses as given by 
Table I. — Summary of Static, Vitro Data 
MDTA LCCA CA 
No. dogs 6 5 5 
Pm (clyne/cm2) X 10-^ „ 149 ± 2 164 ± 2 176 ± 9 
L(em) 7.9 ± .1 1.97 ± .09 3.63 ± .11 
Rme;m(cm) 0.677 ± 0.024 0.145 ±.01 0.232 ± .004 
R/h - 9.5 ±1.0 6.71 ± .53 9.50 ± 1.28 
Xz 1.50 ± 0.07 1.53 ± .05 1.63 ± .04 
\d - 1.48 ± 0.00 1.58 ±.09 1.50 ± .07 
Eo(dyne/cmJ X 10-" 7600 ± 900 7700 ± 2200 14800 ± 3100 
Ez (dyne/cm=) X 10-= 6900 ± 900 38000 ± 11000 8700 ± 2000 
Average values ± SE are shown. MDTA = middle descending 
thoracic aorta; LCCA = left coronary circumflex artery; CA = right 
common carotid artery; Pm — mean pressure; L = length; Rmcan — 
mean value of midwall radius, R; h = thickness. ,\/, and Xe are the 
extension ratios in longitudinal and circumferential directions. Eo 
and Ez are the incremental elastic moduli in circumferential and 
longitudinal directions. 
