556 
HEMODYNAMICS 
each frame of the film. These markers enabled 
the precise synchronization of the analog data 
with the appropriate frame of the film. Selected 
sections of both the dorso-ventral and the corre- 
sponding lateral cineogram were digitized. The 
end of each roll of film contained a calibration 
grid which was used to correct for geometric 
and spherical distortion of the digitized data. 
Calculations 
A) Calculation of spatial distance between 
two points on biplane film. 
D = V (X2 + X^y- (Y, + Yi)2 - (Z2 + Za)2 
where Xn, Yn, Z,, are the coordinates of a given 
point in a cartesian coordinate system in space. 
(1) 
B) Calculation of the average stresses at the 
left ventricular equator. 
Walker, Hawthorne and Sandler^^ have de- 
rived formulae for calculating the average mer- 
idional and hoop stress at the equator of the left 
ventricle. 
The average meridional stress is the force per 
unit area acting at the midplane of the heart in 
the direction of apex-to-base length. This for- 
mula was derived by equating the meridional 
wall forces to the pressure loading assuming 
the ventricle to be a surface of revolution and 
expressed in terms of wall thickness. 
0"m 
P 
Ri 
H 
PRi/2H (1 + H/2Ri) (2) 
average meridional stress (Gm/cm^) 
left ventricular pressure (Gm/cm^) 
internal radius (cm) 
wall thickness (cm) 
The average hoop stress is the force per unit 
area in the circumferential direction. Walker et 
al. have derived an equation for the calculation 
of this stress at the equator, assuming bending 
moments and shear stresses may be neglected. 
o-H = 
PRi 
H 
1 + (H/2R,)^ Rj j J 
O-H = average hoop stress (Gm/cm^) 
P = left ventricular pressure (Gm/ cm^) 
Ri = internal radius (cm) 
H = wall thickness (cm) 
B = V2 length of the ventricle (cm) 
C) Calculation of left ventricular internal 
volume. The internal volume of the left ventri- 
cle was calculated according to the method sug- 
gested by Hunter, Cothran and Hawthorne" 
using the prolate ellipsoid as a geometric model 
of the left ventricular chamber. 
V = 4/377 (Ri)3 B (4) 
Ri = internal transverse radius (cm) 
B = ratio of major to minor axis 
RESULTS 
The geometric changes accompanying con- 
traction of the left ventricle were studied by the 
direct application of dimension transducers to 
the internal and external surfaces of the heart 
and by visualization of radiopaque markers 
using biplane cineradiography. 
Figure 4 exhibits the changes in left ventric- 
ular circumference, wall thickness, pressure 
and the aortic pressure in a dog representative 
of those which were instrumented for such re- 
nin III 
^.v«-..a, 
(3) 
Figure 4. — A representative recording of aortic pres- 
sure (AP), left ventricular pressure (LVP), left 
ventricular wall thickness (LVWT) and left ventric- 
ular circumference (LVC). 
