Fitting procedures, activation analysis

Kinetic analysis based on the Langmuir-Hinshelwood model was performed on the assumption that ethylene and water vapor molecules were adsorbed on the same active site competitively [2]. We assumed then that overall photocatalytic decomposition rate was controlled by the surface reaction of adsorbed ethylene. Under the water vapor concentration from 10,200 to 28,300ppm, and the ethylene concentration from 30 to 100 ppm, the reaction rate equation can be represented by Eq.(l), based on the fitting procedure of 1/r vs. 1/ Ccm ... 

Besides the compartment analysis, non-compartment models can be used. One frequently used procedure is the regression method. This method performs a linear regression fit on a voxel basis. The slope image provides information about the trapping of the tracer, while the intercept image reflects the distribution volume of the radiopharmaceutical. Another non-compartment model is based on the calculation of the fractal dimension (FD) (17). FD is a parameter for the heterogeneity and is calculated for the time-activity data of each individual VOI. The values of FD vary from 0 to 2 showing the deterministic or chaotic distribution of the tracer activity. We use a subdivision of 7 x 7 and a maximal SUV of 20 for the calculation of FD. 

The interpretations given by Kinoshita et al. [32] and Watanabe et al. [34,35] to the peculiar trend of the variation of specific activity as a function of particle size for oxygen reduction reflect two different approaches and two different ways to explain the same behavior. In their analysis, the relationships derived are based on the fitting of curves that actually show significant scattering. Since the experimental procedures to determine the active surface areas and the specific activities are quite standard, this would indicate the presence of additional phenomena. 

---