40 THE MECHANISM OF THE CIRCULATION. 



THE PRESSURE AND WORK OF THE HEART. 



The average mean arterial tension in the brachial artery of a healthy 

 young man is 11 to 12 cms. Hg, and it is probably not much higher in 

 the aorta. If the intraventricular pressure be taken as equal to 

 13 cms. Hg, the pressure exerted by every square centimetre of the 

 inner wall of the left ventricle can then be reckoned thus 



P= 13 cms. x 13 - 5 (sp. gr. of Hg) = 175 P 5 grms. per sq. cm. 



It is obvious that, other things remaining equal, the greater the 

 superficial area of the inner wall, the greater will be the total stress 

 on the ventricle. 



The positive tension of a membrane enclosing a fluid under any given 

 pressure is not a fixed quantity, but, as the radius of curvature at any 

 part of the membrane is greater, so is the tension greater. On account of 

 the larger size of the filled intraventricular cavity, and necessarily greater 

 radii of the curvature of its walls, the distended heart must make a far 

 greater effort at contraction, in order, by means of the tension of its 

 walls, to raise the contained blood to the pressure of that in the aorta. 

 The thinner the heart wall, the fewer the muscle fibres in a given width 

 of its transverse section, the more will each fibre have to exert itself to 

 bring about a given tension. When the exertion of each individual 

 fibre is taken as constant, the fluid pressure per unit area must vary 

 inversely as the cube of the radius of curvature, or, if the pressure be 

 regarded as constant, the exertion of each fibre must vary as the cube 

 of the radius of curvature. If the cardiac chamber be considered a 



2te 



sphere with a wall of uniform substance and elasticity, 1 then P = 



approximately, where P = the blood pressure sustained by each unit 

 of surface of the cardiac w T all ; t = the muscular tension per unit of 

 section ; e = the thickness of the cardiac wall at any time ; and r = the 

 radius of the cardiac chamber at the time. Now e, when the wall is 



thin, varies as -=, therefore P varies as . 

 r 2 T A 



For example, if the auricle contract and reduce its diameter by 

 one-half, it would be able to increase the intra-auricular pressure 

 eightfold, supposing the force of contraction of its constituent muscle 

 fibres remained constant. Sam ways 2 suggests that an auricle, towards 

 the latter part of its contraction, might thus have the advantage over 

 a full ventricle, and continue in certain cases to force blood therein, 

 even after the systole of the ventricle had begun. 



On the other hand, if the auricle or ventricle be suddenly enlarged 

 to twice its diameter, the muscle fibres must be exerted eight times as 

 much as before, to produce the same pressure. It is perhaps on account 

 of this relation between the radius of curvature, and the work of the 

 muscle, that the thickness of the musculature of the ventricle varies 

 more or less directly as the radius of curvature at any point. The 

 columnse carnese and papillary muscles, by acting as stays, also com- 

 pensate for the disadvantage attending the distension of the cavity at 

 the beginning of systole. At the end of systole, when the radii of 



1 The application of this formula to the heart can be only approximately correct, since 

 this condition is only partially fulfilled. 



2 " Le role de 1'oreillette gauche," Paris, 1896, p. 36. 



