Rebreathing in the Mapleson A, C and D breathing systems with sinusoidal and exponential flow waveforms

Abstract

SummaryThe degree of rebreathing in Mapleson A, C and D breathing systems for sinusoidal and exponential flow waveforms is analysed mathematically. The effects of altering the I:E ratio and of introducing an expiratory pause are investigated. The results for sinusoidal waveforms closely resemble those for a square wave. Exponential flow waveforms produce results similar to triangular flow waveforms. The Mapleson A system is always the most efficient. The Mapleson C system is efficient when the I:E ratio is 1:1, becoming less efficient with longer expiration and very inefficient with an expiratory pause. The Mapleson D system becomes efficient when the expiratory pause is long. A previous paper presented a mathematical analysis of rebreathing in the Mapleson A, C and D breathing systems [1]. Only linear flow waveforms were analysed, but the method was shown to predict correctly the behaviour of the breathing systems for a range of respiratory patterns [2]. In this paper, the equations developed earlier are solved for spontaneous ventilation with sinusoidal and exponential flow waveforms. Examples of such waveforms are shown in Fig. 1. For the purposes of this analysis, perfect plug flow (i.e. no longitudinal mixing) is assumed. Describing rebreathingThe efficiency of a breathing system depends on the volume of alveolar gas that is voided. The degree of rebreathing in such systems is conveniently quantified as the ratio of total deadspace to tidal volume (V Dtot /V T ), as described by Jaeger & Schultetus [3]. It varies among breathing systems because gas supplied during part of the respiratory cycle is wasted [1]. This may be analysed by dividing the respiratory cycle into phases, summarised here and defined in the glossary. The respiratory cycle is the inspiratory time (T I ) plus the expiratory time (T E ). Inspiration can be subdivided into the time for which gas flows (T If ) and any inspiratory pause (T Ip ) so T I ¼T If þ T Ip . Similarly, expiration comprises the time for which gas flows (T Ef ) plus the expiratory pause (T Ep ) soThe first part (V y ) of the inspired tidal volume is destined to enter the alveoli and the following part (V z ) will come to lie in the deadspace. T If is thus further divided into T Iy , the time to inspire the alveolar portion and T Iz , the time taken to inspire the deadspace portion of the tidal volume.The terminal part of expiratory flow is of key importance. In the Mapleson C system, it is denoted V nC and represents alveolar gas voided from the system. In the Mapleson D system it is called V nD and represents alveolar gas that will be re-inspired. The time required to expire V nC or V nD is T nC or T nD , respectively.If the inspiratory flow is initially low there is a period at the beginning of inspiration when the expiratory valve remains open and gas is being voided from the system. The volume of fresh gas voided in this way in the Mapleson A system is termed V Iw and in the Mapleson C system is

Impact of respiratory motion correction on SPECT myocardial perfusion imaging using a mechanically moving phantom assembly with variable cardiac defects

“…The breathing cycle and tidal volume followed a sinusoidal exponential pattern. 13 Two electro-proportional valves, controlled by the respiratory pattern equation in the PLC, regulated the air pressure with respect to time, entering in the lungs for inhalation and escaping from the lungs for exhalation, respectively (Figure 1B). This was achieved using two small pumps with suction and blowing ports that could be used as vacuum pumps and small compressors.…”