Therefore, τ for O2 is equation(5) τO2≈VAV˙A, For the soluble gas N2O, using the values of the above variables given in Gavaghan and Hahn (1995), (4) can be re-written as VA′=VA+0.43. Therefore τ for N2O is equation(6) τN2O=VA+0.43V˙A. We can express the ventilation rate V˙A by (Williams et al., 1994) equation(7)

V˙A=R(VT−VD),where R is Selleck PS 341 the respiration rate in breaths/min, VT is the tidal volume, and VD is the airway dead space volume. At high frequencies ω, the term ω2τ2 dominates the denominator in (2), therefore allowing τ to be estimated using equation(8) ΔFAΔFI→1ωτ,where ΔFA, ΔFI, and ω are known values. The estimated τ is then subsequently used to determine lung volume VA using (3) and (4). Conversely, at low values of ω  , the term λbQ˙PV˙A dominates the denominator in (2), and therefore reveals information concerning Q˙P. This indicates that careful selection of ω   allows the variable determination of both lung volume V  A and lung perfusion Q˙P. Hahn et al. (1993) found that the forcing sinusoidal frequency should be f>1min−1, when N2O is used as the forcing gas. Lung volume VA derived from a continuous ventilation model is greater than the actual VA, due to the assumption that VA is constant. In reality, the lung volume including dead space volume VD varies tidally between (VA + VD) at the beginning of inspiration and (VA + VD + VT)

at the end of inspiration. Sainsbury et al. (1997) showed that subtracting a correction term Vc from the lung volume determined 17-AAG by the continuous ventilation model produces a more realistic estimate of the lung volume, equation(9) Vc=12(VT+VD) Etofibrate In our proposed new system, we have used both O2 and N2O to estimate V  A and Q˙P. With the indicator gas O2 regarded as a non-soluble gas with λb ≈ 0, (2)

therefore becomes equation(10) ΔFAΔFIO2=11+ω2τO22,where (ΔFA/ΔFI)O2ΔFA/ΔFIO2 indicates ΔFA/ΔFI obtained using O2 data. From (5) and (10), we have equation(11) VA=V˙AT2πΔFAΔFIO2−2−11/2where V˙A is given by (7), and T is the forcing sinusoidal period in minutes; i.e., T = f−1 = 2π(ω)−1. Here we have reached the estimate of lung volume VA, using (11). For the soluble indicator gas N2O, (2) can be re-written as equation(12) ΔFAΔFIN2O=11+0.47(Q˙P/V˙A)2+ω2τN2O2From (5), (6), (10) and (12), we have equation(13) Q˙P=V˙A0.47ΔFAΔFIN2O−2−VA+0.43VA2·ΔFAΔFIO2−2+VA+0.43VA21/2−1,where V˙A is given by (7), and VA is given by (11). A set of V  A and Q˙P can be produced at any sinusoidal period T, using (11) and (13) where both O2 and N2O contribute to the estimation. In previous work concerning the continuous ventilation model (Hahn, 1996 and Hamilton, 1998), only one type of indicator gas was used, hence V  A and Q˙P had to be estimated separately. One contribution of the proposed system is that, for the first time, V  A and Q˙P can be estimated at the same time using the continuous ventilation model, and this therefore reduces the time to obtain estimates V  A and Q˙P.