916 PHYSIOLOGY 



where W stands for work, w for the weight, and Q for the quantity (volume 

 in c.c.) of blood expelled at each contraction ; R is the average arterial 

 resistance or pressure during the outflow of blood from the heart, and V is 

 the velocity of the blood at the root of the aorta. In this equation QR is 



wV 2 

 the work done in overcoming the resistance,* and is the energy expended 



*g 



in imparting a certain velocity to the blood. 



If we take 60 c.c. as the average output of each ventricle, 100 mm. Hg. 

 as the average pressure at the beginning of the aorta, and 500 mm. per 

 second as the velocity imparted to the blood thrown into the aorta, we can 

 calculate the work done by the human heart at each beat. 



QR 60 x 0-100 m. X 13-6 81-6 grammetres, 

 or roughly 80 grammetres. On the other hand, the expression 



wV 2 60 X (0'5) 2 



= ^^ '- = 0*7 grammetres. 



<2g 2 x 9*8 



It is evident that this latter factor is negligible, and that for all practical 

 purposes we may regard the work of the heart as proportional to the output 

 multiplied by the average arterial blood -pressure. Taking the average 

 pressure in the pulmonary artery at 20 mm. Hg., the work of the right 

 ventricle at each beat would amount to about 16 grammetres, a total for 

 the two ventricles of about 100 grammetres per beat, which is equivalent 

 to about 10,000 kilogrammetres in twenty-four hours for a man at rest. 



This work is done by a contraction of the muscle fibres surrounding the cavities 

 of the ventricles. It is important to remember that the strain or tension which is 

 thrown on these fibres and which resists their contraction will simply be determined not 

 by the blood-pressure which has to be overcome, but also by the size of the ventricle 

 cavities. Since the pressure in a fluid acts in all directions, the tension caused by any 

 given pressure on the walls of a hollow vessel will increase with the diameter of the 

 vessel. Thus if we take a sphere with a radius of 10 cm. filled with fluid at a pressure 

 of 10 cm. Hg. there will be a pressure on each square centimetre of the inner surface 

 of the sphere of 136 grm. The total distending force, i.e. the pressure on the whole 

 of the inner wall of the sphere, will be equal to this pressure multiplied by the area, 

 i.e. to 136 x 4rrr 2 136 x 4?r X 100. If by a contraction of the walls the radius be 

 reduced to 5 cm., the total pressure on the internal surface will be reduced to 

 136 x 4?r X 25, i.e. will be one quarter of the previous amount. Moreover in the case 

 of the heart, with increasing distension the wall becomes thinner and the number of 

 muscle fibres in a given area fewer, so that the larger the heart the more strongly will 

 each fibre have to contract in order to produce a given tension in the contained fluid. 

 At the beginning of systole the distended heart must therefore contract more strongly 

 than at the end of the systole, in order to raise the blood it contains to a pressure 

 sufficient to overcome that in the aorta. 



18 This expression, QR, is only approximately correct. Supposing the pressure in 

 the aorta at the beginning of systole is 50 mm. Hg. and at the end of systole 150 mm., 

 the work could not be deduced accurately from the average pressure, but would need a 

 simple application of the integral calculus for its determination. The expression 

 employed above deviates from the real value only by about 10 per cent., and is therefore 

 sufficiently accurate for our purpose. 



