INTERPRETING PENH IN MICE

To the Editor: In the October 2002 issue of the Journal of Applied Physiology, Lundblad et al. (18) described experimental work that concluded with criticism of the use of the enhanced pause (Penh) variable to estimate airway resistance. In the same issue, an editorial by Hantos and Brusasco (16) supported this criticism. Although we also agree that Penh is not a very reliable respiratory variable, we feel that the criticisms leveled against it in these two articles were perhaps a bit too polite. In fact, there are several concerns with the work by Lundblad et al. that led the authors to overestimate considerably even the small importance of Penh that they found. In the discussion below, we very briefly review some salient points that bear directly on this issue.

Part of the dilemma over what Penh actually measures arises from the well-accepted use of the same plethysmograph pressure to measure tidal volume (7, 19, 23). Tidal volume measurements made with this method in the mouse provide values that are consistent with more direct measurements and mammalian scaling (23). Such a volume measurement, however, appears to be in contrast to the measurement of airway resistance in humans, as originally described by Dubois et al. (8). This classic method involves placing a human in a closed box and using the recorded box pressure to quantify airway resistance. However, procedures that use this approach in humans, that is, breathing at very high frequencies and very low tidal volumes, have been carefully designed to maximize the resistive component of the pressure while minimizing the tidal volume component. Because this method requires voluntary modifications of breathing, it obviously cannot be done in any experimental animal. As we will show, the extent to which this minimization occurs in a mouse breathing normally is in fact negligible.

	SIMPLE THEORETICAL CONSIDERATIONS

Although Lundblad et al. (18) described the theoretical basis of the pressure in the plethysmograph, we need to briefly restate these considerations here in even simpler terms. The setup is to place a mouse inside of a box. During inspiration it is observed that the box pressure rises, and during expiration the box pressure falls. The rise in pressure during inspiration can occur for two very different reasons. The first is that tidal air, as it moves from the box into the lungs, is warmed to core body temperature (37°C) and humidified to 100% relative humidity by the time gas reaches the alveolar spaces. These effects result in an increase in water vapor pressure and a thermal expansion of gas, both of which increase pressure in the plethysmograph box. The larger the tidal volume, the larger the pressure increase, with other factors being equal.

The second reason for an inspiratory increase in box pressure is a decompression of alveolar gas. This effect is easily appreciated if an inspiratory effort is made against a closed glottis or upper airway. The gas in the lung will expand in proportion to the fall in alveolar pressure with the inspiratory effort and the magnitude of lung volume. If we now allow inspiration to occur during the inspiratory effort, there will still be some decompression of the alveolar gas, now in proportion to the inspiratory flow rate and resistance of the airways.

In the following sections, we present calculations to estimate the relative magnitudes of each of these inspiratory pressure components for a quietly breathing mouse in a sealed 300-ml plethysmograph. Regarding these simplified calculations, two points are worth noting. First, the size of the plethysmograph is not critical because both pressure components vary inversely with the box size. Thus comparison of the relative magnitudes will be unaffected. Second, when dealing with an animal in a body box, there is one important concern that is nearly always ignored: the pressures on inspiration and expiration are not symmetrical. That is, with ambient temperature less than body temperature, the pressure rise on inspiration is always greater than the fall on expiration. Two reasons are responsible for this observation: the first is that the box temperature slowly rises because of the animal's presence, and the second is that the drying and cooling of the expired air in the nasal passages cause less of a pressure drop on exhalation. This latter effect was elegantly analyzed by Epstein and Epstein (10); however, because it is not easy to measure the water vapor pressure or temperature of exhaled air in most species, especially the mouse, the corrections they derived have not been utilized. We do not know precisely how much this effect applies in the mouse; however, on the basis of their equations and nominal values, the pressure fall on expiration might be as much as 30-50% smaller than that on inspiration. To avoid worrying about this unpleasant effect and drift in the box pressure, nearly all investigators simply ignore the problem by putting a small hole in the box, thereby creating a high-resistance leak to "stabilize" the pressure trace. It is also worth noting here that the effect of alveolar gas compression on expiratory box pressure will also be smaller than that on inspiration because the peak expiratory flow is normally less than peak inspiratory flow. Our general quantitative conclusions, therefore, would not be greatly changed if we had enough information to do the more detailed calculation on expiration.

Tidal volume expansion. On the basis of the original analysis in the 1955 paper of Drorbaugh and Fenn (7), the following formula can be used for the pressure increase during inspiration

where VT is tidal volume, Tbox and Tlung are temperature (°K) in box and lung, respectively, PB is barometric pressure, PH₂O,box and PH₂O,lung are water vapor pressure in box and lung, respectively, and Cgas is compliance (mostly adiabatic compressibility) of the air in the plethysmograph (~75 ml · cmH₂O¹ · l¹).

Alveolar decompression. The increase in Pbox during inspiration from alveolar decompression is given by the following simple equation based on Boyle's law
where PA is the maximal decrease in alveolar pressure, VL is lung volume at end inspiration, and Vbox = 300 ml.

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	DISCUSSION

These simple theoretical calculations, using physical chemical laws and nominal widely accepted values for mouse lung function, show that, at baseline, the pressure component resulting from airway resistance is at least an order of magnitude smaller than that from expansion of the tidal volume. We say at least an order of magnitude smaller because, by using an estimate of airway resistance from our own laboratory that is almost double what several other laboratories have found after correcting for tissue resistance (22, 24), we may have substantially overestimated the magnitude of the decompression component. Indeed, this conclusion is supported by the results of a clever study done by Enhorning et al. (9). They set up a mechanical bellows, connected inside the box with an equivalent airway resistance, that could be oscillated in a mouse plethysmograph at various breathing frequencies and volumes; they compared these pressure excursions with those from a live mouse. Although the conclusions reached by these investigators were that the pressure increments from tidal volume and decompression were about equal, the mechanical lung had a volume that was much greater than that of a mouse lung. The bellows that they used to simulate the lung had a volume of 6 ml, or at least 12 times a mouse end-inspiratory volume. Because the magnitude of the decompression component of box pressure is directly proportional to the ratio of lung to box volume, this increased mechanical "lung" volume thus led them to overestimate the contribution of the decompression pressure by an order of magnitude. This recalculation thus makes their experimental results quite consistent with our conclusion based on the simple equations above.

From our simple theoretical considerations above and the experiments of Enhorning et al. (9), the original question remains as to why Lundblad et al. (18) concluded that the decompression component was one-third of the total box pressure. They based this conclusion on the results of their experiments in which the temperature in the body box was raised to 37°C in an effort to completely eliminate the pressure component resulting from tidal volume expansion. There are several reasons why this experiment would have substantially overestimated the box pressure component that resulted from airway resistance. First, they made no measurement of the animals' body temperatures. When the box temperature is raised to 37°C, it is very likely that the animal's core body temperature rises above this value. Second, they did not measure or control the box relative humidity. When the ambient temperature is heated, the relative humidity will fall. Both of these effects, however small, will maintain some finite fraction of the tidal volume pressure component. In addition, because the tidal volume pressure component starts at about 10 times greater, one does not need much of this component to have a very big effect. Even a 97% reduction of the magnitude of this tidal pressure component would still result in it being at the level found by Lundblad et al. (i.e., ~30% of the decompression component). A third reason that may have led to an overestimation of this decompression component relates to the calculated external resistance required by the experimental preparation, including the tracheotomy tube and connecting tubing. As was noted some years ago by Chang and Mortola (3), the resistance of a tube in the trachea may be considerably higher than that measured outside. The magnitude of this factor in the mouse airway is not certain, but it could have led to an increased resistive component in the calculations.

As emphasized by Hantos and Brusasco (16), measurement of airway responsiveness in mice adds a critical functional component to many studies that involve genetic and chemical manipulations. In an early study of the genetic variation in mouse airway responsiveness, mice were anesthetized and mechanically ventilated to assess the response of airway smooth muscle to acetylcholine (17). This procedure, as well as others that directly measured lung resistance (2, 5, 13, 22, 25), required killing that animal after the measurement. This necessity limited the usefulness in long-term studies, especially if one had required measurements at many time points. Although it is possible to intubate mice and measure airway smooth muscle responsiveness without causing death (1), this still requires animals to be anesthetized. Thus the research community showed great interest in the 1998 paper by Hamelmann et al. (15), which described the use of a commercial plethysmograph that had the promise of being able to assess responses of airways noninvasively in conscious animals. The dimensionless parameter, Penh, was defined from the box pressure waveform, and a correlation with the other more direct indexes of airway responsiveness was found in their experiments. After publication of this article, we sent a brief letter to the journal questioning how it was possible that the same pressure that had been used successfully for many years in many species to measure tidal volume could now be used to measure airway resistance (21). It seemed to be the ultimate dream variable for physiologists, one that could be used to extract information on whatever one wanted to know. Despite this early concern with the use of Penh, many investigators studying lung function in mice have been seduced by its noninvasive simplicity and have chosen to rely on this method (4, 6, 12, 14, 26).

The results presented here clearly show that, with a mouse undergoing baseline quiet breathing, the pressure in the body plethysmograph that results from the size of the airways is trivial. This is an important result that impacts on the interpretation of studies that use indexes such as Penh to assess changes in airway responsiveness. In most such studies, changes are assessed by normalization to the baseline Penh. It makes no scientific sense, however, to compare such changes with a baseline variable that has nothing to do with airway size. This is true even if there is a large increase in the decompression component. With a large increase in airway resistance, the fraction of box pressure that arises from the resistance will of course increase, and this might be detectable, assuming that there were no other changes in tidal volume or breathing pattern. This assumption, however, is not supported by observation, so even the ability to quantify the absolute effect is scientifically suspect.

One additional concern with the paper by Lundblad et al. (18) is that the investigators never actually measured Penh in their experimental animals. Although their theoretical calculations support the results presented here, that box pressure contains essentially no information about airway size, it would have been helpful to see how Penh changed as the box temperature was raised. Perhaps one reason they avoided this calculation is that the method to calculate it has never been clearly defined. Published works that use Penh cite the Hamelmann et al. paper (15), but, as we also noted previously (21), their description of the calculation is inadequate. As we have described above and also as clearly shown by Lundblad et al. (18), box pressure rises during inspiration and falls during expiration. Figure 2 in Hamelmann et al., which is used to describe the Penh calculation, does not show this. And furthermore, because most box pressure traces from a conscious animal in the box show rapid up-and-down oscillating pressure, such as that shown in Fig. 3a of Hamelmann et al., there is no obvious way to apply the analysis in their Fig. 2 to make a Penh calculation from such a trace. Perhaps Lundblad et al. also felt it impossible to make such calculations, but this was not discussed.

Finally, it is worth noting that, given the demand for rapid screening of mouse pulmonary function, the situation of using Penh to assess mouse pulmonary function has almost reached epidemic dependency. After a presentation critical of the use of Penh by one of us (Mitzner) at a minisymposium on lung mechanics in the mouse at the 2002 American Thoracic Society meeting, someone asked the following: if indeed Penh was not a useful measurement of airway responsiveness, what could be used instead? The company for which the questioner worked required measurements of airway responsivity in mice, and the questioner almost demanded us to provide an alternative. It appears that current desires and needs to have some easy, unthinking way to assess mouse lung function have created a Penh addiction in many investigators. Unfortunately, we regret to report that, at the present time, there is no physiological methadone to treat this addiction.

Perhaps one thing investigators might do to maintain some perspective is not to use the term Penh. Giving this nonsense variable a unique name that resembles a pressure makes it too easy to misinterpret quantitative changes that, in fact, have no relation to the size of the airways. An observed doubling of Penh has no more information about the airways than a tripling of Penh because, as noted, the baseline measurement contains essentially no information content about airways. If investigators cannot control their need to measure this, we would suggest calling it ventilatory timing (e.g., like expiratory time) or simply ventilation. Then at least one may be less likely to misinterpret experimental results. Observations of increased "ventilatory timing" after some intervention or challenge might then lead one to attempt to make meaningful quantitative measurements that relate to airway size. Of course, this approach will still totally miss those situations in which airways are affected with minimal ventilatory effects, but this may be the price one pays for addiction.