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4, 6, and 7. The relative error ��rA = ��rA/rA, was calculated as a measure of sensitivity of rA estimation to uncertainty in model parameters and to the value of rA itself. The model was constructed using a priori values for parameters (rD, rS, ��, PS = PAO2) and their respective variations shown in Table 1. An additional analysis was performed to evaluate model sensitivity to ignoring VS by building the model using http://www.selleck.cn/products/Romidepsin-FK228.html rS �� [0.1, 10] and solving for rA by setting rS ��. The accuracy of rA estimation was also evaluated with respect to SNR of the second image with magnetization MA(2) = r �� rS �� MS (rS http://www.selleckchem.com/products/nutlin-3a.html these regions are more ��signal-demanding�� than normal regions in regard to measurement accuracy. In consideration of the effects of ventilation deficiency, this measure of SNR provides a conservative assessment of sensitivity to noise. Noise was introduced in the noise-free simulated model by adding a normally distributed noise (25) to the second image, with zero mean and a proper variance to yield the desired SNR value. The same noise variance was then http://www.selleckchem.com/products/AC-220.html randomly added to all images in the sequence. Each noise level was simulated 1000 times to yield a statistically plausible result. Finally, a similar analysis was performed using a partial number of ventilation images to assess the robustness of the model to the number of included images in the presence of noise. Regardless of the actual magnetization buildup in the airways, the apparent MRI signal observed at the end of each breath is a function of the applied flip angle �� to acquire the image. As it is demonstrated by simulation in Fig. 3c and d, the flip angle value has a significant nonlinear effect on the rate of HP gas signal buildup in the airways. As is evident by Eq. 3, using a too small value for �� (e.g., less than 1��) results in a diminished MR signal, which in turn adversely affects the reliability of parameter estimation from the model. A too large value for �� (e.g., larger than 10��) causes an excessive RF signal decay of the residual magnetization at each step (i.e., the MA(j-1) term in Eq. 2). This results in a significant decrease of signal buildup and makes it impractical to extract the fractional ventilation information from the sequence of images. Therefore, �� value has to be selected such that both criteria are satisfied. Signal buildup, on the other hand, is tightly related to rA, which in turn affects the choice of ��.