NEWS AND VIEWS

Model lung breathes true

An interesting calculation of how the human lung functions has appeared in an Italian journal whose fortunes appear (from inspection) to be reviving.

ONcE upon a time, in the 1950s, II Nuovo the lung, turbulent motion and convection made. Cimento shared with the Japanese journal are chiefly responsible for gas transport, The outcome of the calculation is much Progress in Theoretical Physics the distinc­ but molecular diffusion dominates in the what physiologists would expect. The tion of being among the most eagerly read alveoli. authors restrict themselves to the case in in its field, but it was then eclipsed by the Bonsignori and Salvini acknowledge which it is supposed that somebody takes emergence of rapid-publication journals that their model is not original, but they in a single substantial breath, holds it for a such as Physical Review Letters and, later, do claim to have improved on earlier cal­ little while and then empties the lungs. of Physics Letters. culations (in the 1970s) by improving on What the solution of the equation shows But Il Nuovo Cimento seems to be perk­ some of the approximations on which is, first, that a component of the inspired ing up. Nowadays, it is almost always pos­ previous calculations have been subject. gas progressively penetrates through the sible to find something of interest in an For one thing, they reckon to have used a system with the passage of time, and that issue. Part of the explanation is that, for better representation of the cross section the process is the more rapid as the in­ the past eleven years, there have been of the lung with distance along the air­ coming flow is faster. four sections dealing separately with ways. More pointedly, they allow for the The supposition that, in the outer nuclear physics, astrophysics, condensed way in which the effective diffusion con­ reaches of the system, the concentration matter and general physics, which means stant can vary with the velocity of the flow of particular components of the inspired that there are in principle four issues a and with place along the airways. In the gas quickly become more or less constant month. In some sections, the publication alveoli proper, the implicit assumption is readily falls out from the calculations, but lag (one of the reasons for the original that the gases in the lung exchange their concentrations in the inner reaches decline) is still uncomfortably long - contents freely with the blood, which is for quickly fall to zero as gas is rapidly some papers seem to take a year in the practical purposes regarded as an infinite absorbed across the alveolar walls. The process of publication But the more obscure reservoir. time constant ofthe system appears to be a backwaters of general relativity on which The objective is to write down and then few seconds-rather more than 4 seconds the journal retained a lien throughout its to solve a differential equation for the dif­ in one significant context-which accords bleak period are no longer the staple diet fusion and convection of gases along the with general experience of trying to hold for II Nuovo Cimento's faithful readers. airways; Bonsignori and Salvini judici­ one's breath. It may or may not be coinci­ Last month's condensed matter issue, for ously discuss the boundary conditions that dence, but the calculations appear to show example, contains an intriguing calcula­ should apply at the walls of the airways, that, when breathing air, the model lung tion of gas transport in the human lung of a acknowledging that in the alveoli, at least, reaches in just over a second a condition in kind that would normally have been found there are grounds for believing that the which the oxygen concentration is vir­ in a physiological journal. concentration of one component of gas tually constant throughout the inner part As F. Bonsignori and M. Salvini, both inspired will be virtually constant along of the respiratory system, taken to be the physicists from the University of Bologna, directions perpendicular to the walls of last seven generations of airway refine­ describe it, the problem is really fairly the alveoli, and that from some point suf­ ment. straightforward (II Nov. Cim. llD, 1247; ficiently deeply buried in the network, the Inevitably, the authors promise to 1989). The trick, which has been used concentration of all components will be produce a second set of more refined before, is to represent the lung and its virtually unchanging in space and time. calculations, paying particular attention airways, the trachea and bronchi, by a But this implies that there are two for­ to the vexed question of the boundary kind of one-dimensional model. They mally different sets of boundary condi­ conditions most appropriate in different follow physiologists in supposing that tions that may be relevant, whence the parts of the respiratory system. At this there are 23 generations of successive re­ suggestion (not further followed up) that stage, however, nothing is said about the finement in the lung, at each of which some mixture of the two would be most assumptions that the gas in the lungs is the total area of the walls across which gas appropriate. incompressible, or that there is no inter­ can be exchanged increases. The problem The variations of the effective diffusion ference between the different components then becomes that of calculating the pro­ coefficient, which determines the effec­ of the inspired gas that people breathe. No cesses by which exchangable gases reach tiveness of mixing under different cir­ doubt the next step will be to collect some the walls of the lung and diffuse through cumstances, are tackled semi-empirically. carefully controlled experimental data in them. In the entering airways, mixing is much the hope of matching calculation and The physiological data used to ground more efficient than would be determined experiment. the model are striking in themselves. The by molecular diffusion, but in the alveoli, The interest of all this is not simply that cross-section of the airways increases from molecular diffusion is king. Part of the it is what seems to be a reasonably realistic 2.54 cm2 in the trachea to 11,800 cm2 at the construction of the equations to be solved calculation of the properties of a compli­ finest and twenty-third subdivision of the entails fixing parameters by reference to cated physiological system, but that it alveoli, whose total volume is a third of the known parameters of the lung, using appears in a straightforward physics jour­ the capacity of the lung as a whole (taken the helpful (and reasonable) conditions nal. No doubt the bibliographic retrievers to be just over 1.5 litres, everything in­ that air should not accumulate anywhere will alert physiologists to what they may cluded). The most obvious consequence in the system. The remarkable feature of otherwise overlook, but that it should of this state of affairs is that gas velocities the calculation is that it leads to an explicit have appeared there at all is a neat sign of progressively decrease from the mouth to result, although one in which several how broadly catholic is the Italian Physical the alveoli, so that in the main airways into numerical approximations have been Society. John Maddox NATURE · VOL 341 · 5 OCTOBER 1989 381 © 1989 Nature Publishing Group