Another problem is the choice of gases when using (28): both CO2 and the indicator gas produce a set of Bohr equations. The estimated values of VD obtained using different gases are usually different from one another, and it is difficult to know which gas produces the more reliable results. A simple average of all the various estimates for each indicator gas may not be sufficiently stable, if some estimates Dabrafenib in vivo are erroneous. To overcome the problems described above, we propose a regression approach to improve the stability of the original Bohr equation. We re-write (28) as equation(29) (FE′−FE¯)=VDVT(FE′−FI′). Each breath produces a set

of values for x   and y  , corresponding to a point on a straight line equation(30) y=ax,y=ax,where

y=(FE′−FE¯), x=(FE′−FI′)x=(FE′−FI′), and a is the slope of the line, a = VD/VT. The optimal value of VD can be determined by finding the value of a that best describes the straight line using linear regression. Values (x, y) of both CO2 and the indicator gas from all breaths are used in the linear regression, in order to achieve a robust estimate selleck chemicals llc that incorporates results obtained using both gases. The proposed method uses all breaths without suffering from the instabilities induced by near-zero values in the original Bohr equation. The results shown in Section 5.2 indicate that using both gases achieves a more robust estimate than using a single gas, and that the proposed linear regression Thalidomide approach is more stable than using a simple average

of estimates obtained using the original Bohr equation. Twenty data sessions from healthy human volunteers were studied, with results obtained from one volunteer studied in detail in this paper, for illustration of the prototype system. Results obtained from all volunteers are then summarised in Fig. 4 and Table 3. Both N2O and O2 are injected as indicator gases. For each of T   = 2, 3, 4, and 5 min, data were collected for 10 min duration. For the tidal ventilation model, the data were divided into 20 data windows (i.e., each window contained 30 s of data); each of these windows of data was used to estimate V  D, V  A, and Q˙P. The mean and standard deviation of these estimates are shown in Fig. 3(a)–(c). The continuous ventilation model requires measurements of ΔFA and ΔFI, and hence the total duration of data was used to produce a single set of estimates for this method, against which our breath-by-breath tidal ventilation model will be compared. As described in Section 2, for the continuous ventilation model, a set of V  A and Q˙P estimates can be produced at any sinusoidal period T, using (11) and (13), where both O2 and N2O estimates contribute to the overall estimates.