Further exploration of the Penh parameter.

Unrestrained plethysmography (UP) has been widely used to measure airway reactivity in conscious mice. It is non-invasive, easy to use, suitable for longitudinal studies, and allows a large throughput of animals for screening purposes. A non-dimensional parameter based on a characteristic change in the expiratory waveshape of the UP box signal, Penh, has been used as an indicator of bronchconstriction. Hamelmann et al. [Non-invasive measurement of airway responsiveness in allergen mice using barometric plethysmography. Am J Respir Crit Care Med 1997;156:766-77] presented experimental data showing a correlation between Penh and intrapleural pressure, as well as lung resistance; and Dohi et al. [Non-invasive system for evaluating the allergen-specific airway response in a murine model of asthma. Lab Invest 1999;79:1559-71] showed that Penh tracked the bronchial response to allergen challenge. More recently, papers and letters to the editor have argued against the use of UP and Penh in resistance applications, presenting mathematical and theoretical arguments that the UP waveform, and parameters derived from it (Penh) are dominated by conditioning, and are essentially unrelated to resistance [Lundblad et al. A reevaluation of the validity of UP in mice. J Appl Physiol 2002;93:1198-207; Mitzner and Tankersley. Interpreting Penh in mice. J Appl Physiol 2003;94:828-32]. This paper discusses the mathematics of UP as applied to two types of whole body plethysmographs (WBPs): a sealed chamber (pressure plethysmograph, PWBP); and a chamber with a pneumotachograph in its wall (flow plethysmograph, FWBP). We show that the PWBP waveform is largely dominated by conditioning, and exhibits little effect due to resistance; thus supporting the claim that UP and Penh are unrelated to resistance, when applied to measurements at typical room temperatures. By contrast, the effects of resistance or specific airway resistance (sRaw) are evident in the FWBP waveform, even at room temperature. Penh is derived from the FWBP waveform. We show that the changes in the FWBP waveform which occur in response to methacholine challenge cannot be due to conditioning, and are not simply due to changes in respiratory timing. Finally, we describe how Penh quantifies those changes.