The gas inspired into the alveolar compartment is in two parts: the first comes from the dead space compartment, and the second is fresh inspired gas. FIA,n(t)

also therefore consists of two parts: the first part has a value of FA,n−1 since this was the alveolar concentration of indicator gas from the previous SCH727965 order breath which now resides in the dead space; the second part has a value of FI,n(t), the concentration of the indicator gas measured by the concentration sensor at the mouth during inspiration of breath n. Here we have made the distinction between indicator gas concentration in the lung and that at the mouth, and therefore FIA,n(t) can be expressed as equation(16) FIA,n(t)=FA,n−1iftbI≤t

dead space during inspiration of breath n. Substituting (16) into (15), we have equation(17) VI=∫tbItbI+TDIV˙(t)FA,n−1dt+∫tbIteI−TDIV˙(t)FI,n(t)dt=VDFA,n−1+∫tbIteI−TDIV˙(t)FI,n(t)dt Here we have arrived at an expression for VIVI. Now we seek to find an expression for VEVE and VQVQ, to complete the conservation of mass equation (14). In the above analysis of the first part of F  IA,n(t  ) in (16), we have assumed that F  A,n (the indicator gas concentration in the lung during breath n  ) is constant during any breath n  ; this means that F  A,n is equal to FE′,nFE′,n (the measured indicator gas concentration at the end of expiration in breath n). That is, equation(18) Screening Library FA,n=FE′,nFA,n=FE′,n The reason for using FE′,nFE′,n here is that it is more readily measured than F  A,n. FE′FE′ (the function of FE′,nFE′,n over all breaths) is a sine wave expressed in Eqs. (25) and (26), using our indicator gas injection method in Section  3.2. Eq. (18) implies that FA (the function of the indicator gas concentration in the lung from all breaths) is also a sine wave. The

expired indicator gas volume VEVE can be expressed as equation(19) VE=VT,nFA,n,VE=VT,nFA,n,where VT,n is the tidal volume (the Clomifene volume of gas inhaled and exhaled) during breath n. Substituting (18) into (19) gives the final expression for VEVE equation(20) VE=VT,nFE′,n.VE=VT,nFE′,n. The uptake of the indicator gas VQVQ is equation(21) VQ=Q˙Pλb(FA,n−FV¯,n)Tn,where Q˙P is the pulmonary blood flow, λ  b is blood solubility coefficient of the indicator gas, and T  n is the duration of breath n  . FV¯,n is the average indicator gas concentration returned to the lung through venous recirculation in breath n. Some of the inspired indicator gas is taken up by the pulmonary capillary blood in the lung, and eventually returns to the lung via venous recirculation. Previous research has shown that at carefully chosen forcing frequencies, the venous recirculation effects can be ignored (Hahn et al.