Biodynamics: Circulation by Y. C. Fung

By Y. C. Fung

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Turning now to the question of stress in the heart itself, there is another very simple anal ysis that is quite good. Assume that the left ventricle can be approximated by a thick -walled hemispherical shell (Fig. 1 : 2), with inner radiu s 0 and outer radius b. Let the pressure acting on the inside be Pi (blood pressure) and that actin g on the out side be Po (pressure from pericardium), both assumed to be uniform . Consider the equilibrium of forces in the vertical direction. The force acting downw ard is equal to Pi times the projected area 2 2 1W .

C is an integration constant. To determine c, let a point be chosen on the curve , so that P = P" when A. = 1,*; then P = (p* + f3)e aO. * ) - f3 . (6) Experimental results on series element show that (Sonnen blick, 1964, Parmley and Sonnenblick, 1967, Edman and Nilsson, 1968) ~~ = rx'(S + fn , (7) 52 2 The Heart where rx ', P' ar e also constants. Hence S is also an exponential function of the extension I] : (8) The contractile element shortening velocity may be represented by the following modified Hill's equation (Fung, 1970) diJ dt b[Sof(t) - S] a+S (9) in which the constants a and b are functions of muscle length L, So is the peak tensile stress arrived in an isometric contraction at length L, t is the time after stimulus, andf(t) is a function which may be represented as f(t) = sin [~(~)l .

The shading increases in darkness with increa sing length of interval s. Fr om W. G. Guntheroth, (1965) Pediatric Electrocardiography , W. B. Saunders Co. , Philadelphia, on the basis of dat a in Scher and Young (1956). Reproduced by perm ission . The bundle of His passes down the right side of the interventricular septum and then divides into the right and left bundle branches. From these further branches called Purkinje f ibers spread over both ventricles. See Fig. 3: 1. Electric signal propagates fast in the Purkinje fibers at a speed of 1 to 4 m/sec.

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