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MECANICA DA RESPIRAÇÃO
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  Mechanics of Breathiq h Man’ ARTHUR B. OTIS, WALLACE 0. FENN AND HERMANN RAHN. From the Department of Physiology and Vital Economics, University of Rochester School of Medicine and Dentistry, Rochester, New York T E MECHANICAL WORK done by the respiratory muscles in producing the movements of breathing has been studied relatively little by physiologists. Although most text-books of physiology give values for the work done by the heart, similar estimates for the work of breathing are lacking. The classic con- tributions of Rohrer (1-3) lay the foundation for this subject, but only a few pertinent papers, notably those of Neergaard and Wirz (4), Vuilleumier (s), Bayliss and Robertson (6), and Dean and Visscher (7), have since appeared. The material presented below, although based on data which are neither sufficiently precise nor extensive enough to furnish an exact description of the mechanics of breathing, constitutes an approximate analysis, which we have found valuable as a way of thinking about certain respiratory problems. FORCES INVOLVED IN BREATHING From the work of previous investigators and on the basis of a priori reasoning, we should expect that the respiratory muscles in carrying out the breathing movements would have to overcome several types of resisting forces. These forces will be mentioned briefly now and considered later in more detail. The chest and lungs are elastic in nature and must be stretched during inspir- ation to accommodate an increased volume. The air in moving through the respiratory tract encounters viscous a.nd turbulent resistance, and there is probably some additional non-elastic resistance associated with deformation of tissues, and with the sliding of organs over one another when they are displaced. Finally, since the system is almost continuously accelerating or decelerating, inertia should be mentioned as a possible factor. The calculations of Rohrer (3)) however, indicate that the force required for acceleration must be ordinarily very small, and we shall, in general, consider it negligible. Another factor of relatively inconsequential magnitude is the kinetic energy imparted to the air. Received for publication March 31, 1950. 1 This work was completed under contract between the University of Rochester and the Air Mate- riel Command, Wright-Patterson Air Force Base, Dayton, Ohio. Some of our earlier work was re- ported in C.M.R. Report No* 430, May 10, 1945 and in Federation PYOC. 6: 173, 1947. A .n abstract of a preliminary report, presented before the National Academy of Sciences, appears in Science 110: 443, 1949-  May I950 MECHANICS OF BREATHING IN MAN 593 Elastic Forces. If a person relaxes his respiratory muscles completely, the lungs assume a volume close to that which is customary at the end of a normal expiration, the mid-capacity or relaxation volume. At this volume the elastic forces of the chest must be equal and opposite to those of the lung. When the chest-lung system is displaced to any other volume, elastic forces which oppose the displacing force are developed. The method of measuring these elastic forces as relaxation pressures and a curve showing the relationship between relaxation pressure and lung volume have been presented in a previous paper from this laboratory (8). The reciprocal slope, AP/AV, of the relaxation pressure curve is the elastic resistance or ‘elastance’ (pressure required to produce unit change in volume (6, 7)). Although the relaxation pressure curve is not linear, it is approximately so over a considerable part of its range, and as a first ap- proximation the elastance may be expressed by the following equation: Pel = KV 0 where K is the elastance and P,l. is the pressure developed when the displace- ment from the relaxation volume is V. Air Viscance and Turbulence. A method for estimating the magnitude of the viscous and turbulent forces that must be overcome in moving air through the respiratory tract has been described previously (9, IO), and data have been presented which indicate that the relationship between these forces and the velocity of air flow may be described approximately by the following equation: Pazc. h(g)+k,(g 0 where Pal,. is the pressure gradient between alveoli and mouth that is required to move the air with a velocity (dV/dt). The constants k1 and & are the air viscance2 and the turbulent resistance, respectively. An example of the sort of record from which data were obtained for purposes of the present investigation is shown in figure I, and the points ob- tained from measurement of records made on subject R are shown in figure 3. The parabola was fitted to these points by the method of residuals. Resistance Associated with Tissue Deformation. It does not seem feasible to measure directly the non-elastic resistance associated with tissue deformation, but an estimate may be obtained in the following fashion. A trained subject is placed in a Drinker respirator and is instructed to relax as completely as 2 Our usage of the word ‘viscance’ in this paper is implicit in equation z and may be used synono- mously with ‘viscous resistance’; it is expressed in dimensions of pressure per unit flow of respired gas. ‘Viscance’ was defined by Bayliss and Robertson (6) as “the viscous force per unit deformation” or “viscous pressure per unit of tidal air volume.” Dean and Visscher (7)) however, use the same term to mean “viscous resistance to a unit velocity of flow.” Although the definition of Bayliss and Robertson was stated to make ‘viscance’ analagous to ‘electrical resistance,’ we believe that our usage of the term is a better analogy.  594 A. B. OTIS, W. 0. FENN AND H. RAHN Volume 2 possible so that his breathing movements are produced by the alternating pressure within the respirator instead of by the action of his respiratory muscles. The pressure gradient between the respirator and the mouth of the subject and the velocity of air flow are simultaneously recorded. The pressure recorded at any moment is, of course, that required to overcome the total resistance, and since the elastance and air viscance and turbulent resistance can be obtained as described above, the non-elastic tissue resistance can be esti- mated by difference. Figure 2 shows a sample record obtained in this type of experiment. Fig. I (left). SIMXJLTANEOUS RECORDS of pressure at mouth (zipper tracing) and pneumotachogram (~OZUY &u&g). In pneumotachogram, inspiration is above and expiration below baseline. Sudden changes in pressure at mouth and simultaneous interruptions of air flow were produced by brief closure of solenoid valve located in airway between mouth and pneumotachograph. Method of esti- mating alveolar pressure (P,z,.) is indicated. Fig. 2 (righl). SIMULTANEOUS RECORDS of pressure gradient between mouth and inside of Drinker respirator (@per tracircg) and pneumotachogram (lezeer tracitig). Subject R. A useful way of representing some of the data that can be obtained from such a record is shown in figure 4 in which pressure is plotted against accumu- lated volume for one breathing cycle. The method of constructing such a diagram will now be described. The velocity of flow and the simultaneous pressure were measured and tabulated for each o.r-second interval of the record of the respiratory cycle shown in figure 3. Then starting at the beginning of inspiration each O.I- second interval of the flow curve was integrated by multiplying the mean velocity of flow during each period by 0.1 second. This gave the volume that flowed during each o.r-second period. These volumes were then added in a cumulative fashion and the total volume at the end of each time interval was plotted against the corresponding pressure gradient that existed at the end of  May 19.50 MECHANICS OF BREATHING IN MAN 595 that interval. The plotted points determine the solid lines that form the large loop in figure 4. This closed curve represents the relationship between the changes in the volume of the lung during the respiratory cycle and the external forces (as represented by the pressure gradient between the respirator and mouth) acting to produce this change. At two moments (when the cycle reverses from in- I I I I I I Fig. 3. RELATIONSHIP between instantaneous rate of flow of respired gas and pressure gradient between alveoli and mouth for subject R. Curve drawn through points represents equation : W4 & 0.5 > 0 0 1234 5 6 7 P ClLV CM. H,O Fig. 4. RELATIONSHIP between volume of respired gas and pressure gradient during one respiratory cycle for Subject R. For explanation, see text. 1. ” I . . . 5 IO 15 PRESSURE C M. H,O spiration to expiration and vice versa) no air is being moved in either direction. At these instants, therefore, the total force acting is being used to maintain elastic tension that has been developed, inertia being assumed to be negligible. If we assume a linear relationship between elastic pressure and lung volume, then the diagonal in figure 4 represents this relationship. Approximately, it is a segment of the relaxation pressure curve. Some of the information represented by figure 4 may be summarized as follows. As the lung volume is increased during inspiration, the total pressure
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