562 
HEMODYNAMICS 
the ventricle in the plane of the minor axis was 
circular. 
These data document the relative contribu- 
tions of transverse and longitudinal dimen- 
sional changes to the geometric alterations oc- 
curring in the left ventricle during systole. The 
changes which we observed in left ventricular 
dimensions indicated that ejection resulted 
largely from a decrease in the internal diame- 
ter. The ratio of internal minor axis shortening 
to major axis shortening averaged 3.5 :1 for the 
group of dogs studied. The ventricular lengths 
measured in these studies lie mainly along the 
outflow tract and exhibit agreement with the 
magnitude of aorta-to-apex length change 
which Hinds^ observed. A consideration of the 
geometric alteration which must accompany 
these dimensional changes during ejection im- 
plies that the inner surface of the ventricle 
must decrease proportionately more than the 
external surface. This implied difference be- 
tween external and internal dimensional 
changes is confirmed by the marked increase in 
wall thickness and cross sectional area seen at 
this time. Our measurements of thickness are in 
general agreement with those of other 
investigators. ^^'^^ The increase in wall thick- 
ness concommitant with a reduction in external 
diameter demonstrates that the major direction 
for wall thickening is toward the lumen. 
The use of thin wall formulae for the meas- 
urement of tension or stress in various struc- 
tures applies only if the ratio of wall thickness 
to internal radius is less than 0.1.^'^ Our studies 
show that this ratio is considerably greater at 
end-diastole and increases markedly during 
ventricular systole. Therefore, we have used 
equations derived by Walker, Hawthorne and 
Sandler^^ which require thickness measure- 
ments in the calculation of meridional and hoop 
stress. The contour of the two stress curves ob- 
tained in this study are alike and bear a marked 
similarity to the left ventricular tension curves 
described by Sandler and Dodge^^ for humans 
and to the mural force curves described by 
Hefner-2 in anesthetized dogs. Of the two 
stresses which were calculated, the hoop stress 
was found to be the larger force. In fact, the 
maximum meridional stress is not significantly 
different from the magnitude of the peak left 
ventricular pressure when expressed in similar 
units of dimension (gm/cm^). It is of interest 
that the average myocardial stresses are declin- 
ing at a time when the left ventricular pressure 
is maximal and sustained. This occurs as left 
ventricular wall thickness approaches its maxi- 
mum. The resultant increase in the cross-sec- 
tional area of the ventricular wall reduces the 
internal cross-sectional area to both lower the 
magnitude of the force acting at the endocardial 
surface and to provide a larger myocardial sur- 
face area across which this force is distributed. 
The measurement of the internal diameter of 
the left ventricle provides a more useful way to 
get at estimates of internal volume than does 
the measurement of external dimensions. This 
is due to the significant changes in the thickness 
of the wall during the cardiac cycle and varia- 
tions in this dimension at different sites. 
Bishop^'^ has reported that a linear relationship 
exists between the moment-to-moment changes 
in the volume ejected from the left ventricle 
and the associated internal diameter. Likewise, 
we have observed this linear relationship in the 
present study. Bishop emphasized in his 
studies that this relationship is not dependent 
upon a constant geometrical shape of the left 
ventricle but rather a constant geometric fac- 
tor. This is supported in part by our observa- 
tion that the axis ratio increases during ejection 
while both the length and internal transverse 
diameter are decreasing. This finding indi- 
cates that the rate and extent of shortening of 
the minor axis exceeds that of the major axis. 
As a result, the ventricle assumes an increas- 
ingly prolate geometry during the time course 
of ejection. 
The observation of a linear relationship be- 
tween the axis ratio and the internal radius of 
the left ventricle during ejection made possible 
the calculation of the attendant internal volume 
from a knowledge of internal radius alone. This 
was done by substitution of the measured inter- 
nal radius into the combination of equations 4 
and 5 and by using the calculated end-diastolic 
axis ratio as a constant in equation 4. Estima- 
tions of the change in internal volume by the 
former method underestimates the actual stroke 
volume by only 3.5% while the latter method 
yields an overestimation of 9.7 % . Both methods 
