AN ANALYSIS OF LEFT VENTRICULAR 
DIMENSIONAL CHANGES IN CONSCIOUS ANIMALS 
L. N. Cothran, E. W. Hawthorne and H. Sandler* 
Experiments were designed and conducted to study 
the continuous changes in left ventricular external and 
internal geometry throughout the cardiac cycle in con- 
scious animals. An analysis of the data obtained from 
typical, normal cardiac cycles revealed an average de- 
crease in the external diameter of the left ventricle of 
3.5%, a 32% increase in wall thickness, an 18% de- 
crease in the internal diameter and a 6% decrease in 
length during the ejection phase. These dimensional 
changes resulted in a 14.6% increase in the internal 
major to minor axis ratio (AR) of the left ventricle. A 
linear relation was found when the instantaneous inter- 
nal radius of the left ventricle was plotted against the 
simultaneously derived axis ratio. The equation describ- 
ing the latter relation was determined to be: Axis ratio 
= — 0.6 Ri -|- 3. By use of this equation to determine 
(AR) and the equation for the volume of a prolate el- 
lipsoid (V = 4/37rRi^AR) a method was derived for 
calculation of the instantaneous internal volume of the 
left ventricle during the ejection period from a knowl- 
edge of the internal radius alone. 
INTRODUCTION 
All of the methods presently available for as- 
sessing the performance of the intact heart re- 
quire either direct information about the size, 
shape and cyclic changes in these variables or 
the use of certain simplifying assumptions 
based in part upon an a priori knovi^ledge of dy- 
namic cardiac dimensions. The size and shape 
of the left ventricle greatly affects its perform- 
ance as a pump and are therefore necessary 
measurements for evaluation of its hydraulic 
functions. Additionally, in order to obtain in- 
formation which would provide for characteri- 
zation of the material properties and basic mus- 
cle mechanics of the left ventricle, dimensional 
measurements are essential. Knowledge of the 
importance of heart size and shape and the ap- 
plication of these variables in determining car- 
diac function is not new. These concepts are em- 
bodied in the application of the law of Laplace^ 
* Howard University College of Medicine, Washington, D. C. and 
NASA-Ames Research Center, Moffett Field, California. 
to the ventricle by Wood- and in the Frank- 
Starling^ mechanism. Therefore, the history of 
cardiac dimensional analysis covers almost one 
century. However, the availability of instru- 
mentation and the techniques for measurement 
of individual chamber dimensions in both hu- 
mans and experimental animals are relatively 
recent. Through the use of such techniques, it 
has been established that marked differences in 
cardiac size and performance become manifest 
when experimental animals are subjected to 
anesthetization and thoracotomy.* Therefore, it 
has been emphasized that the most meaningful 
way of determining the mechanisms operative 
in the moment-to-moment control of ventricular 
functions is to obtain an accurate estimate of 
the performance of the heart in intact, un- 
anesthetized animals.^ 
The application of linear dimensional meas- 
urements of the left ventricle to estimates of in- 
ternal volume requires the development of geo- 
metric analogs to represent the ventricular 
chamber. A number of geometric models of the 
left ventricle have been proposed and used to 
derive estimates of chamber volume, muscle 
mass and the magnitude and distribution of 
forces within the wall. The derivation of equa- 
tions for calculating these variables is depend- 
ent upon the geometric model which is em- 
ployed. The models most frequently used for 
these purposes have been a sphere, cylinder, 
cone, paraboloid and the ellipse of revolution. 
Dodge et al.*' have determined the ratio of ma- 
jor-to-minor axis of the human left ventricle at 
end-diastole and end-systole and suggested the 
simplest geometric shape equivalent to that of 
the left ventricle to be a prollate ellipsoid. This 
observation has been supported by Hawthorne'^ 
from studies of the external left ventricular di- 
mensions of dogs and by Gorlin^ who used the 
same data corrected for wall thickness to obtain 
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